Mehdi Rahmani

This paper presents a robust predictive load frequency control for power systems with uncertain parameters and time delays in communication networks. The goal of the proposed approach is to achieve good performance for the closed-loop system under practical problems of the network including uncertainties in the dynamic model, time delays in the system, and time-varying model. To this end, a decentralized state-feedback control law is obtained by solving an linear matrix inequality based optimization. The aim of the optimization problem is to regularize the frequency deviation with the minimum control effort. It is shown that the stability of the system is guaranteed with respect to the Lyapunov stability theorem. Moreover, the problem is reformulated as a centralized load frequency control (LFC) approach for single-area power systems, and also as a non-predictive LFC method with lower computational complexity. The performance and robustness of the proposed strategy are studied through simulation results in different cases of uncertain and time-varying single-area and multi-area power systems with time delays.

Unbalanced development of Alborz Province in recent years has amplified groundwater security crisis as well as water stress. This study conducted dynamic decision support system modelling of sustainable groundwater resources management based on water-food-energy security nexus (WFESN-SD-DSS). Using the results, the scenarios were designed in three categories of solutions: 1- Groundwater resources security; 2- Groundwater resources security; and 3- Groundwater resources security. The WFEN-SD-DSS model findings implied that combined policies represented the best solution and these included: Aquifer artificial recharge of 10 million cubic meters per year; control of well water usage; exploitation and reuse of graywater to supply 10% of agricultural water; 10% development of irrigation efficiency using novel irrigation systems; 10% reduction of agricultural waste; 10% development of the performance of agricultural products by modifying seeds, conserving plants; 5% reduction of electrical energy dissipation in combined cycle power plants; and development of solar water pump systems in agriculture sector.

The amount of waste electrical and electronic equipment (WEEE) has been rapidly growing in recent years. Estimation close to reality of the future amounts of WEEE as a function of time is critical to effective their management. Wastes from mobile phones and computers are one of the several subgroups of WEEE. The objective of this study was to estimate past and future trends in the generation of obsolete computers and mobile phones in Iran. For this purpose a combination of two models were used. At the beginning, time-series multiple lifespan model was used to estimate outflows end-of-life obsolete equipment. Then, using the simplified logistic function model by Excel software, the values of obsolete computers and mobile phones in the future were estimated. The study found that the amount of E-waste generation in the country was 20 million wasted computers until 2016 and 39 million wasted mobile phones until 2014. Results of the time series model analysis showed a total amount of 2.8 million waste computers would be reused by 2016 and 4.2 million mobile phones would be reused by 2014. The results of the logistic equation indicate that by the year 2040 there will be 50 million units of obsolete computers. According to the same model 90 million mobile phones will be obsolete by 2035. Increase in the number of computers and mobile phones was fitted into the logistic model and the results showed that the saturation level of generation of obsolete computers and mobile phones are 24 and 21 years respectively following the base year 2016 and 2014.

This paper proposes an LMI approach to model predictive control of nonlinear systems with switching between multiple modes. In this approach, at each mode, the nonlinear system is divided to a linearized model in addition to a nonlinear term. A sum of squares (SOS) optimization problem is presented to find a quadratic bound for the nonlinear part. The stability condition of the switching system is obtained by using a discrete Lyapunov function and then the sufficient state feedback control law is achieved so that guarantees the stability of the system and also minimizes an infinite prediction horizon performance index. Moreover, two other LMI optimization problems are solved at each mode in order to find the maximum area region of convergence of the nonlinear system inscribed in the region of stability. The performance and effectiveness of the proposed MPC approach are illustrated by two case studies.

In this paper, the dynamic output feedback control problem for uncertain network control systems in the presence of constraints on network communication channels is investigated. These limitations include time-varying delays, packet dropouts, and quantization in both communication channels from sensor-to-controller and controller-to-plant. Packet dropouts are modeled by i.i.d Bernoulli processes. Also, logarithmic quantization and time-interval delays are considered in the communication network. To ensure the robust mean square stability and H∞ performance of the closed-loop system under imperfect communication channels, a dynamic output feedback control approach based on H2/H∞ criteria is proposed in the framework of linear matrix inequalities. A numerical example is presented to illustrate the validity of the theoretical analysis, and applicability of the proposed control approach.

Abstract Weldlines are inescapable byproducts of the injection molding process. They represent potentially fatal flaws particularly in multiphase materials. In this work weldlines in injection molded glass fiber‐reinforced polypropylene (0 to 40wt%) were studied as a function of the cavity shapes and depths. It was found that the weldline is a zone between 2 and 8 mm wide extending throughout the thickness in which the fibers are oriented almost perfectly in a plane parallel to the weldline. While the strength of moldings without weldlines depends on the mold shape and on the fiber concentration, the weldline strength is a function of fiber content only. A simple model based on the assumption of complete debonding of the fiber‐matrix interface when failure occurs can be used to predict the strength loss in the weldline.

In large-scale power systems, classical centralized control approaches may fail due to geographically distribution of information and decentralized controllers result in sub-optimal solution for load–frequency control (LFC) problems. In this paper, a two-level structure is presented to obtain optimal solution for LFC problems and also reduce the computational complexity of centralized controllers. In this approach, an interconnected multi-area power system is decomposed into several sub-systems (areas) at the first-level. Then an optimization problem in each area is solved separately, with respect to its local information and interaction signals coming from other areas. At the second-level, by updating the interaction signals and using an iterative procedure, the local controllers will converge to the overall optimal solution. By parallel solving of areas, the computational time of the algorithm is reduced in contrast to centralized controllers. This approach is applicable to any interconnected large-scale power system. However, for simulation purposes, a three-are power system is presented to show advantages and optimality of the proposed algorithm.

The design of robust model predictive controller (RMPC) for uncertain nonlinear system is a challenging problem in the area of nonlinear control, yet. A new approach to RMPC is presented here for nonlinear systems with state-dependent uncertainties. The nonlinear system is considered as comprised of a linear part, a nonlinear term, and a bounded additive uncertainty. A state feedback control law is obtained via solving an optimization problem of an infinite horizon quadratic cost function in the framework of linear matrix inequalities (LMIs). To solve the optimization problem, the nonlinear and uncertain terms of the system are supposed to be bounded by a quadratic function that is obtained by solving a sum of squares (SOS) optimization problem. Moreover, the sufficient state feedback synthesis condition guarantees the robust stability of the system in the presence of unknown bounded uncertainties. In this context, a LMI-based optimization problem is solved to obtain the maximum region of stability which is desired to be a subset of the region of feasibility. The simulation examples are reported to indicate the applicability and effectiveness of the proposed approach with different uncertainty scenarios.

This paper proposes a distributed robust Kalman filter for time-varying uncertain linear multisensor systems subjected to stochastic uncertainties. A consensus algorithm is utilized to compromise on a single data among information of all nodes in a multisensor system. Distributed filtering based on consensus remarkably stands out from other algorithms because each node not only estimates its local states correctly, but also reaches an agreement with other nodes over a sensor network as well. The distributed filtering problem is formulated here using consensus on estimation (CE) algorithm. The optimal parameters of the filter are computed by minimizing the covariance of the estimation error. Moreover, the stability of the touched upon algorithm is proved by the Lyapunov stability theorem. Simulation results for a multisensor system with 100 nodes are presented to show the effectiveness and performance of the proposed CE-based distributed robust filtering approach.

Summary In this paper, the problem of robust distributed H ∞ filtering is investigated for state‐delayed discrete‐time linear systems over a sensor network with multiple fading measurements, random time‐varying communication delays, and norm‐bounded uncertainties in all matrices of the system. The diagonal matrices, whose elements are individual independent random variables, are utilized to describe the multiple fading measurements. Furthermore, the Bernoulli‐distributed white sequences are introduced to model the random occurrence of time‐varying communication delays. In the proposed filtering approach, the stability of the estimation error system is first shown by the Lyapunov stability theory and the H ∞ performance is then achieved using a linear matrix inequality method. Finally, two numerical examples are given to show the effectiveness and performance of the proposed approach.

In this paper, we propose a robust hybrid state estimation (RHSE) algorithm to redress the presence of bounded data uncertainties (BDU) using SCADA measurements and phasor measurement units (PMUs). To address it, we modify the formulation of weighted least squares (WLS) method in a robust manner to eliminate the effect of uncertainty in both measurements and network parameters. The IEEE 30–bus system subject to uncertainty is considered as the simulation case to study the performance of the proposed RHSE approach and to compare the desirable results with the existing estimators. In the following, the impact of the number of PMUs on the performance of the proposed method is also investigated.

In this paper, the robust filtering problem for uncertain complex networks with time-varying state delay and stochastic nonlinear coupling based on H∞ performance criterion is studied. The random connections of coupling nodes are represented by utilizing independent random variables and the multiple fading measurements phenomenon is characterized by introducing diagonal matrices with independent stochastic elements. Moreover, the probabilistic time-varying delays in the measurement outputs are described by white sequences with the Bernoulli distributions. Furthermore, All system's matrices are supposed to have uncertainty and a quadratic bound is assumed for nonlinear part of the network. This bound can be obtained by solving a sum of squares (SOS) optimization problem. By applying the Lyapunov theory, we design a robust filter for each node of the network so that the filtering error system is asymptomatically stable and the H∞ performances are met. Then, the parameters of the filters are achieved by solving a linear matrix inequality (LMI) feasibility problem. Finally, the applicability and performance of the proposed H∞ filtering approach are demonstrated via a practical example.

Abstract This study presents a systematic methodology for developing a stabilizing controller for a general hybrid systems model. The approach is based on utilizing the small‐gain theorem as a means of constructing the Lyapunov function and analyzing the input–output stability of the subsystems in the feedback loop. By considering the control system in a closed‐loop configuration with the hybrid system, the small‐gain theorem can be applied. In this scheme, a dynamic control system is proposed that satisfies the closed‐loop stability conditions. This method applies to various hybrid systems' applications due to its generality. To demonstrate the effectiveness and performance of the proposed control approach, two simulation examples, including a linear hybrid system and a bipedal walking robot, are examined.

Economic nonlinear model predictive control is a great choice to tackle the control issues appearing in the current wind energy industry. In this paper, instead of generator power, aerodynamic power is employed in the economic cost function to establish the required conditions of stability and convergence of the economic performance, such as turnpike and problem convexity. However, since aerodynamic power depends on time-varying wind speed, conventional time-invariant economic nonlinear model predictive controllers cannot guarantee the stability and convergence of economic performance. This paper proposes a new time-varying economic nonlinear model predictive controller for wind turbine control that considers an economic trajectory, instead of a steady-state, in its optimization problem. The proposed time-varying economic cost function directly considers aerodynamic power, the activity of pitch angle and generator torque, and fatigue loads on the shaft and tower. Therefore, this controller can maximize power extraction and reduce fatigue load on the tower, drivetrain, and actuators. Furthermore, a fast-parallel Newton-type method is used to implement the proposed controller in actual wind turbines. An accurate aeroelastic model is used to validate the performance of the proposed control scheme. The proposed controller is also compared with two tracking nonlinear model predictive controllers, the baseline controller, and a newly developed method, under fatigue and extreme load scenarios in the presence and absence of uncertainty. The simulation results show the superior economic performance of the proposed approach. Moreover, the real-time results verify the computational speed that the proposed controller requires to deploy actual wind turbines.

Finding an optimal control strategy for a nonlinear uncertain system is a challenging problem in the area of nonlinear controller design. In this paper, a two-level control algorithm is developed for robust optimal control of large-scale nonlinear systems. For this purpose, using a decomposition/coordination framework, the large-scale nonlinear system is first decomposed into several smaller subsystems, at the first level, where a closed-form solution as a feedback of states and interactions is obtained to optimize each subsystem. At the second level, a substitution-type prediction method, as a coordination strategy, is used to compensate the nonlinear terms of the system and to predict the interaction between subsystems. The coordinator mainly evaluates the next update for the coordination parameters and continues to exchange information with the first level, so that the overall optimum solution is obtained. This approach is applicable to any large-scale nonlinear uncertain system with unstructured bounded uncertainties. The effectiveness and performance of the proposed approach are investigated through simulation of a nonlinear quadruple-tank process.

In this paper, a new robust distributed model predictive control (RDMPC) is proposed for large-scale systems with polytopic uncertainties. The time-varying system is first decomposed into several interconnected subsystems. Interactions between subsystems are obtained by a distributed Kalman filter, in which unknown parameters of the system are estimated using local measurements and measurements of neighboring subsystems that are available via a network. Quadratic boundedness is used to guarantee the stability of the closed-loop system. In the MPC algorithm, an output feedback-interaction feedforward control input is computed by an LMI-based optimization problem that minimizes an upper bound on the worst case value of an infinite-horizon objective function. Then, an iterative Nash-based algorithm is presented to achieve the overall optimal solution of the whole system in partially distributed fashion. Finally, the proposed distributed MPC approach is applied to a load frequency control (LFC) problem of a multi-area power network to study the efficiency and applicability of the algorithm in comparison with the centralized, distributed and decentralized MPC schemes.

This paper proposes a recursive filter for discrete-time linear dynamic systems subject to output outliers or heavy-tailed noises. First, we introduce a weight matrix in the conventional MAP estimation. It is shown that this matrix plays an influential role in the innovation whitening and asymptotic variance of the modified MAP estimation and, consequently, can be used in outlier detection. Then, we propose two different constrained optimization problems to obtain this weight. These constraints, stemming from environmental noise characteristics, help to obtain the weight matrix more precisely, which increases the filtering performance significantly. In the first approach, we introduce a convex optimization problem to minimize the estimation upper bound of the error covariance matrix. The second approach converts the modified MAP estimation to a min–min optimization problem with a concave cost function. Consequently, to reduce the effect of outliers in estimation, a semidefinite program (SDP) is proposed for outlier detection. At last, simulation results show the effectiveness and verify the performance of the proposed filter for dynamic systems in the presence of measurement outliers.

The augmented state robust regularized least-squares filter (ASRRLSF) and two-stage robust regularized least-squares filter (TSRRLSF) are proposed for discrete time-varying nonlinear systems with unknown inputs and norm-bounded uncertainties. Unknown inputs affect both state-space model and measurements equation of the system. Combining system states and unknown inputs as an augmented state, the ASRRLSF is developed by converting a deterministic min–max optimization problem to a robust regularized least-squares problem. If dimension of the augmented state increases, the performance of the proposed ASRRLSF will reduce and the computational cost will increase rapidly. Therefore, in the following, the TSRRLSF is proposed by decoupling the ASRRLSF to lower order filters as system states filter and unknown inputs filter using T transformation. Finally, two numerical examples are given in order to illustrate the performance of the proposed filtering approaches.

In this paper, a new robust Kalman filter is proposed for discrete-time time-varying linear stochastic systems. The system under consideration is subject to stochastic and norm-bounded uncertainties in all matrices of the system model. In the proposed approach, the filter is first achieved by solving a stochastic min–max optimization problem. Next, we find an upper bound on the estimation error covariance, and then, by using a linear matrix inequality (LMI) optimization problem, unknown parameters of the filter are determined such that the obtained upper bound is minimized. Finally, two numerical examples are given to demonstrate the effectiveness and performance of the proposed filtering approach compared to the existing robust filters.

A new analytical-graphical method is proposed for computing the region of stability for proportional-integral-derivative (PID) controllers based on the Hermite–Biehler theorem. By this method, a PID controller is designed to ensure the Hurwitz stability of a time-delay system with any order of transfer function. First, the possible range of the derivative part that makes the system stable is obtained. Then, the stability region is found by applying the Hermite–Biehler theorem. It is shown that this theorem can be extended to quasi-polynomials functions in the form of ψ(ν,eν) to find the stability region of systems with time delay under certain conditions. Using this, the proposed approach can guarantee specified gain and phase margins for time-delay systems; therefore, it is very beneficial and advantageous for the control of practical plants. Five different examples including two practical systems are studied throughout the paper to illustrate the applicability, performance, and efficiency of the proposed control approach.

Abstract A new method has been introduced to predict the power of important classes of energetic compounds including nitroaromatics, acyclic and cyclic nitramines, nitrate esters and nitroaliphatics. In this method, the predicted specific impulse and the corrected heat of detonation on the basis of H 2 O‐CO 2 arbitrary decomposition, have been used to calculate the power of an explosive with the molecular formula C a H b N c O d as determined by the Trauzl test. The predicted results show good agreement with respect to the measured values for both pure and mixture of explosives. The calculated volume expansions of pure energetic compounds have a root mean square (rms) deviation of 33 cm 3 from 73 measured values (corresponding to 58 molecules). For 9 explosive mixtures, the predicted volume expansions have an rms deviation of 39 cm 3 from the experimental results.

A robust Kalman filter is proposed for time-varying discrete-time linear systems with uncertainties in state, input noise, and measurement matrices. The filter is obtained by solving an optimisation problem such that the upper bound on the variance of estimation error to be minimised for all admissible uncertainties. A numerical example is presented to show the performance of the proposed robust filter.

This paper proposes a linear matrix inequality (LMI) approach to mixed-integer model predictive control (MPC) of uncertain hybrid systems with binary and real valued control inputs. The stability condition of the hybrid system is obtained by using the Lyapunov function and then a sufficient state feedback control law is achieved so that guarantees the closed-loop stability and also minimises an infinite horizon performance index. The primal optimisation problem is convex, therefore, a convex relaxation is investigated by introducing the Lagrange dual function. The real and binary control inputs are obtained by solving the dual of the dual problem in the framework of LMIs. The performance and effectiveness of the proposed MPC approach and the duality gap of the convex relaxation are studied through simulation results of a hybrid system with mixed real and binary inputs.

Abstract In this paper, the state estimation problems, including filtering and one‐step prediction, are solved for uncertain stochastic time‐varying multisensor systems by using centralized and decentralized data fusion methods. Uncertainties are considered in all parts of the state space model as multiplicative noises. For the first time, both centralized and decentralized estimators are designed based on the regularized least‐squares method. To design the proposed centralized fusion estimator, observation equations are first rewritten as a stacked observation. Then, an optimal estimator is obtained from a regularized least‐squares problem. In addition, for decentralized data fusion, first, optimal local estimators are designed, and then fusion rule is achieved by solving a least‐squares problem. Two recursive equations are also obtained to compute the unknown covariance matrices of the filtering and prediction errors. Finally, a three‐sensor target‐tracking system is employed to demonstrate the effectiveness and performance of the proposed estimation approaches.

The problem of distributed state estimation for time-varying uncertain systems over a sensor network within the robust Kalman filtering framework is studied. It is assumed that the parameters of the underlying model are subjected to stochastic uncertainties. At the first step, the authors present a particular form of the Kalman filter named information form of a robust Kalman filter. Then, using a consensus scheme that guarantees an agreement in estimation among nodes, they propose a new consensus-based robust filtering approach. The consensus methodology is a hybrid method that is a combination of consensus on information (CI) and consensus on measurement (CM). To this end, before proposing the hybrid consensus filtering algorithm, distributed robust filtering based on CI and CM have been presented. Next, they show that the estimation error in the proposed consensus algorithm is exponentially mean square bounded using a Lyapunov function. Finally, they provide two illustrative examples to show the robust performance and effectiveness of the proposed consensus filtering algorithms.

One of the most important problems in the estimation theory is the one-step prediction. The goal of this problem is to determine the predictions of states in the next time step. This paper focuses on the one-step prediction for nonlinear dynamic systems. The system under investigation involves unknown inputs and the system noises are correlated. In this approach, using the Taylor series expansion for nonlinear functions, a new augmented state nonlinear predictor is proposed for discrete time-varying nonlinear systems. This predictor is obtained by solving a deterministic min-max optimization based on the regularized least squares problem. Moreover, to reduce the computational complexity of the prediction solution, using a nonlinear transformation, we propose a two-stage predictor including lower order estimators for states and unknown inputs. Finally, a frequency modulated signal model is considered to illustrate the effectiveness and performance of the proposed approaches in comparison with the existing estimation methods.

This paper considers a constrained co-design problem for linear time-invariant (LTI) systems. With a practical vision of real-world problems, constraints on the control signal and system states are involved in the proposed algorithm. The main goal is to design a sub-optimal controller by simultaneously obtaining the control policy and the model parameters. To this end, the conventional problem of solving the Hamiltonian-Jacobi-Bellman (HJB) equation is transformed into a nonlinear non-convex optimisation problem. Then, by reformulating the constraints of the optimisation problem, it is relaxed into a convex Semi-Definite Programming (SDP). By presenting an iterative method, the control cost, the performance, and the number of iterations are improved compared to conventional methods, and a closer result to the optimal solution is obtained. The performance and efficacy of the proposed algorithm are investigated through a case study on the physical load positioning system.

This paper presents a new approach to predict the strength of energetic compounds in which there are important classes of high explosives including nitroaromatics, acyclic and cyclic nitramines, nitrate esters and nitroaliphatics. For CaHbNcOd compounds, the ratio of carbon to oxygen atoms and the predicted heat of detonation on the basis of the H2O–CO2 arbitrary have been used to calculate the strength of an explosive. The new model can give good predictions for mentioned energetic compounds as determined by the Trauzl test. The novel correlation will be useful in predicting the strength or power of a new energetic compound that has significant potential in the field of explosives and propellants.

Abstract This study aimed to investigate the effect of cognitive behavioral training on depression in Hemodialysis patients selected hospitals in Mashhad was. For this purpose the number of cases in 1210 haemodialysis patients in 12hospitals in Mashhad dialysis with random (cluster) from 12 hospitals, four hospitals selected from among 40 cases of patients selected for the study and random assignment in the two groups…. (20 patients) and control ( n  =  20) groups. Training patterns of cognitive behavior therapy for experimental group and control group were not given training in this study significant amount of pre-test and post test results from t-test Msql criteria. Results indicate the experimental group had reduced depression and cognitive behavior training effect on haemodialysis patients was felt depressed.Recent research results highly consistent with results Sylvyra Priscilla Dvarth et al (2009) has a total of this study indicate Asrgzary cognitive behavioral patterns in hemodialysis patients is to reduce depression.

IET CommunicationsVolume 13, Issue 13 p. 1971-1979 Research ArticleFree Access Collaborative data aggregation using multiple antennas sensors and fusion centre with energy harvesting capability in WSN Correction(s) for this article Erratum: Collaborative data aggregation using multiple antennas sensors and fusion centre with energy harvesting capability in WSN Volume 14Issue 3IET Communications pages: 539-539 First Published online: February 1, 2020 Morteza Choubin, Morteza Choubin Department of Electrical Engineering, Imam Khomeini International University, Qazvin, IranSearch for more papers by this authorAbass Taherpour, Corresponding Author Abass Taherpour taherpour@eng.ikiu.ac.ir Department of Electrical Engineering, Imam Khomeini International University, Qazvin, IranSearch for more papers by this authorMehdi Rahmani, Mehdi Rahmani Department of Electrical Engineering, Imam Khomeini International University, Qazvin, IranSearch for more papers by this author Morteza Choubin, Morteza Choubin Department of Electrical Engineering, Imam Khomeini International University, Qazvin, IranSearch for more papers by this authorAbass Taherpour, Corresponding Author Abass Taherpour taherpour@eng.ikiu.ac.ir Department of Electrical Engineering, Imam Khomeini International University, Qazvin, IranSearch for more papers by this authorMehdi Rahmani, Mehdi Rahmani Department of Electrical Engineering, Imam Khomeini International University, Qazvin, IranSearch for more papers by this author First published: 01 August 2019 https://doi.org/10.1049/iet-com.2019.0004Citations: 2AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In this study, the authors study the collaborative data aggregation using multiple antennas sensors and fusion centre (FC) with energy harvesting capability in the wireless sensor network (WSN). The optimisation problem is formulated to improve the data transfer rate, based on the parameters of collaboration among sensors, the energy harvesting, and storage of each sensor. In particular, they observe several practical constraints for energy harvesting and capability battery energy storage to maintain network connectivity. They propose three scenarios based on the number of antennas for transferring, collecting, and sharing the data on sensor and FC. It is shown these optimisation problems are a non-convex and to resolve this issue, the objective function is converted to a convex function using a relaxation method. The numerical results show the impact of different parameters on the data rate at FC and improvement in network connection and throughput by using proposed collaborative data aggregation techniques compared to their counterparts. Nomenclature N number of sensor T number of time period fundamental data K number of antenna at FC sampling time of data collecting and energy harvesting rate transmission of data collecting sharing time of energy and data rate transmission of data sharing receiving time of the data to FC rate transmission of the data transferred to FC measurement noise channel coefficients between IoT and sensor measurement coefficients of IoT matrix of collaboration coefficients between sensors measurement coefficients between sensors channel gain between sensors and FC receiver noise fading channel gain average distance among each sensor and the th antenna of FC channel fading factor among the sensor and the antennas of FC received signals at FC amount of harvested energy average rate harvested energy charging and discharging sensor (energy storage value) limitation of battery capacity keeping limitation minimum of network energy cost collaboration link coefficient correlation of collaboration link location of sensor ith 1 Introduction In internet of things (IoT), a set of digital devices (e.g. digital watch, sensor shoes etc.) always sends data with different power values to the scenarios at different distances in time. Nowadays, energy efficiency is one of the important issues in the analysis and design of wireless sensor networks (WSNs) in order to improve rates and service quality [1, 2] Based on the Erickson technical report [3], over 50 billion devices, such as sensors, smartphones, and medical and wearable devices, will be connected to the internet by 2020. Obviously, to serve such device networks, the energy consumption of future networks will be increased significantly compared to the existing networks. It is very important to notice that most sensors work with limited battery capacity. In order to solve these problems, wireless power transfer is a suitable method for harvesting (e.g. the radio frequency energy from the received signal). This method increases the lifetime of WSNs. By using the wireless energy transfer (WET), electromagnetic energy can be transferred to rechargeable batteries by radio waves through air media without a connected line. Based on the simplicity and access to user experiences, some researchers have studied the WET algorithms, technologies, and applications in WSNs. Network architecture for the wireless rechargeable sensor networks (WRSNs) was introduced by describing the performance of the permanent operation for WRSNs and was analysed. The design of algorithm and network principles of WET for specific communication networks was studied in [4]. In [5], a favourable time switching state was suggested to achieve an agreement between the wireless information and energy harvesting. Since radio signals simultaneously carry radio data and energy, coherent wireless information and power transfer (SWIPT) has recently been presented and attracted much attention from both academia and industry. A SWIPT should be able to decode the information and harvest the energy from a signal. However, it could not be implemented, because there are limitations in the design of the receiver's circuit [6]. The problem of energy effect optimisation for SWIPT was recently considered in [7-9]. In [7], a collaborative energy transfer problem in SWIPT system in clustering sensor networks was formulated to create a distribution repetition algorithm in power allocation, power splitting, and relay selection. In [8], the resource allocation algorithm was studied to maximise the power effect of data transfer in orthogonal multi-frequency systems by the SWIPT. Lee and Hong [9] studied the allocation plan of efficiency energy resources for the SWIPT by estimating the incomplete channel and determining the training interval. In [10], the energy efficiency and three factors of spectral energy, transfer power, and outage target rate are considered for two different modes including power splitting, and time switching modes in the receiver. Note that these effects focus on how to achieve the energy rate demand. However, a compromise between energy efficiency and spectral efficiency and the problem of energy efficiency optimisation in SWIPT for WSNs with FCs full of multiple antennas have not been considered yet. In addition, implementation of the environmental standard turned out to be significantly difficult, and led to increasing the required costs of energy optimisation for wireless networks. In [11], the formation of energy beams in multi-user systems is studied based on time-division multiple access (TDMA) with a feed centre of power. Time allocation and the design of an energy beam formation as a non-convex problem were performed to maximise the output of the whole system. In addition, the suboptimal relaxation method was implemented for converting a problem to a convex problem. Furthermore, the simulations showed that the complexity of implementation was significantly reduced. Krikidis [12] focused on the effect of collaboration and relay selection in a network with a large dimension by SWIPT. The study focused on the network with a lot of random sender–receiver paired relays (hop) and reception and retransfer relays. The power required to keep both types of converters and relays was supplied through wired connections. The power of receivers used power splitting. In addition, energy harvesting and quality of service as two limitations of radio frequency were estimated. Moreover, the policy of random relay selection was studied based on a divided area with the central angle in the direction of each receiver. The sources' transmissions were supported by a random number of potential relays that were randomly distributed into the network the closed-form function performance was obtained from system Rayleigh fading network with separated information and energy harvested in each receiver. Liu et al. [13, 14] investigated both energy harvesting and collaboration among the sensors. They showed that energy harvesting can increase the stability of the network. In these studies, multiple antennas were not considered at FC to optimise the sensor network. Moreover, the improvement in sending and receiving rates was not investigated. In this regard, if the approach in [15] is applied to the above methods; a solution will be obtained for FC multiple antennas. To summarise the above discussion, the previous studies in this topic did not consider optimal number of antenna on sensors of data transmission, the effect of change in threshold coefficient of battery capacity for keeping minimum limitation of a network, the effect of change in maximum limitation of the storage threshold, and the effect of change in signal-to-noise ratio (SNR) in the WSN model. Furthermore, there were no available links for some sensor nodes, and the connected sensors have data and energy links. This study takes into account all above issues; in addition, considers the collaboration among sensor and storage energy of each sensor in WSN as variables of the optimisation problem to improve the rate of data transmission. The problem is solved in three different scenarios based on the number of antennas on the sensor for transferring, collecting, and sharing data. The numerical results show the impact of the parameters on the performance rate by using distributed spatial diversity of FC multiple antennas and the collaboration in the data collection and energy harvesting among sensors. Therefore, the main focus of our discussion is to establish the improvement data rate in WSN. For this purpose, the SWIPT technique is considered as an effective method to improve the performance of WSNs with limited energy supply. Moreover, the optimisation of energy efficiency to design the SWIPT in rechargeable sensor networks has not been studied from a green communication perspective yet. In this study, it was assumed that the time distances are independent of each other. 1.1 Motivation and major assumption In most studies involving the network resources, the focus is not on the resources allocation. In most cases, there are inadequate and inefficient approaches to energy efficiency, power consumption, and resource allocation that required solving the problems using FC multiple antennas and sensor antennas. We summarise the contribution of this work as follows. • New system model: In this study, we consider three steps in the model of the WSN. The first step is the data collecting and energy harvesting, the second step is the data and energy sharing and collaborating, and the last step is the data transmission to FC. • Using multiple antennas on each sensor and FC: In this study, due to the advances in sensor generation, multiple antennas are inserted in each sensor. In order to utilise the diversity properties used in similar multiple-input multiple-output networks, we benefit from power transferring and data receiving at FC. The effect of using multiple antennas is to improve data reception at FC from sensors using the coherent multiple access channel (MAC). • Using energy transmission antennas to share energy in sensor networks: Given that limitation of minimum energy is necessary for each sensor, it should be used the feature of energy sharing in the sensor network to improve the power consumption of each sensor. Using energy harvesting in this approach makes it possible to use the network more efficiently. • Using collaboration among sensors to remove limitation in battery size: In this approach, the problem constraints include limitations of storage resources (batteries) in energy harvesting and limitations in keeping network to be activated and preventing network disruptions. The use of the transmission of energy and data among neighbouring sensors in the sensor network improves the transmission and receipt of information flow in the sensor network. We use energy harvesting to keep the network active, and remove the limitation in battery size. • The optimal collaboration to data and energy sharing for data aggregation and transmission rate in WSN: In this study, optimisation coefficients are obtained using the ability of energy harvesting (EH) and WET of each sensor, the collaboration between sensors in data sharing, and FC multiple antennas using optimal calculation feedback from the FC. 1.2 Paper organisation In the following, Section 2 defines the proposed system models. Reformulation and simplification using matrix vectorisation are reported in Section 3. The proposed states are defined in Section 4. The optimisation problem is presented to achieve collaborative data aggregation in Section 5. Simulation and numerical results are analysed in Section 6. Finally, the conclusion is given in Section 7. 1.3 Paper organisation Table 1 shows the applied parameters used throughout this paper. Table 1. Table of constraints relationships in other references for WSN Equations Reference [13] [13] [19] [20] 2 System model In this model, multiple antennas on each sensor are working independently at different distances of time. In all states, every time period is assumed to be the same. Time distances and activity of each sensor in a time period are presented as follows. Both data collecting and energy harvesting are operated from the IoT in the first time distance (). In the second time distance (), energy and data sharing are operated among sensor nodes in the network. The data are transferred to FC in the last time distance (). Now, let us define , , and . Since the data collected from IoT of sensors with additive white Gaussian noise (AWGN), the measurement vector for the nth sensor at time is as follows [14]: (1)where is the measurement vector, is the vector coefficients between IoT and sensors, is the interest parameter with the distribution , is the noise vector with independent and identically distributed Gaussian random variables with the element of noise vector for and . The value of the data rate for the channel with AWGN is obtained by the following capacity formula for normalised bandwidth spectrum [16]: (2) (3)where , and are the rates of data collection, variance of fundamental data, variance of measurement noise, and the total power, respectively. Note that the most effective parameters in this equation is . In the second phase, the following relationship is used to share the data and energy among the sensors. The collaboration among sensors is represented by a understood matrix with zero-one entries, i.e. for and . In topology matrix , means that the nth sensor shares its data and energy sharing with the mth sensor, and shows the lack of a collaboration link from the nth sensor to the mth sensor [14]. The bidirectional communication link between two sensors indicates that the underlying graph of the network is conducted but not fundamentally connected. In particular, the network granted by for communicates to the amplify-and-forward transmission procedure considered in [17]. In addition, for exposes the link of connection between FC and the nth sensor. Based on the topology matrix, the collaboration process of sensors at time distance is given by [17] (4a) (4b)where , is the collaborative signal at the nth sensor and time t, is the collaboration weights matrix, , , denotes the element-wise product, is the vector of all ones, and is the matrix of all zeroes. During this step, the data sharing rate with other sensor states within the network is obtained by the following capacity formula for normalised bandwidth spectrum [16]: (5) (6)where , and show the transmission rate of energy and data sharing, SNR in collaboration state, number of sensors that connected together and the additional noise variance in the sensor network, respectively. Obviously, in this equation, the value of is considered the main variable for the data rate. After sensor collaboration in data and energy, the message is transmitted through a coherent MAC to the FC. So that each of the received signals of (4b) is as follows [15]: (7)where , is gain of channel between nth sensor and kth antenna time distance , is considered the additional noise with distribution for fading channel at kth antenna of FC. Note that each element of is defined for a fading channel as follows [18]: (8)where is a distribution complex fading channel gain and is the average distance between each sensor node and the kth antenna at FC that with the uniform distribution is the channel fading factor among the sensor nodes and the antenna of FC. The transmission rate of FC is obtained from the subsequent capacity formula for normalised bandwidth spectrum [16]: (9) (10) (11)where is the received SNR at FC, is the transmission gain at time t, is the gain of the channel between the th sensor and the kth antenna at time distance , represents the variance of additive noise at FC and is the number of connected sensor nodes to FC and other collaboration coefficients between sensors are transmitted through these links, too. In [13], a variable was introduced for the charging and discharging operations of the nth sensor at the tth time, and the following subscript for sign on the charging and discharging of the battery was given by [13]: (12)There is a capacity bound of the storage of sensor, i.e. the sum of stored energy must always be less than a threshold denoted by . To increase the networks lifetime, it is also desirable to have some maintenance stored energy, denoted by , at the end of the sampling, sharing and transferring time for data. Given the harvested energy and the operating mode of the energy storage of sensors, the energy consumption for sensor collaboration and data transmission satisfies the constraint in Table 1. The relationships of limitations in other references for WSN are also reported in this table. 3 Reformulation and simplification using matrix vectorisation In this section, we simplify problem (4b) using the sparsity structure of the topology matrix and concatenating the non-zero entries of a collaboration matrix, , into a collaboration vector, , where L is the total number of non-zero entries in the adjacency matrix [14, 20]. In (4b), the optimisation variables are the non-zero entries of the collaboration matrix. We concatenate these non-zero entries into the following collaboration vector: (13)where denotes the lth entry of , and is the number of non-zero entries of the topology matrix . Fig. 1 shows the vectorisation of through an example. The matrix is (14)Consequently, the collaboration matrix is given by (15)where is the number of sensors nodes that three nodes communicated to FC. The relationship between and is presented in the following lemma. Lemma 1.The functions and are rewritten as functions of (16)where and are known coefficients, matrices and are given by (17)for and , and are determined by for . Proof.See [14, Section III-A]. Fig. 1Open in figure viewerPowerPoint Vectorisation example of Based on Lemma 1, the data rate of collaboration among sensors (6), the data rate at FC (11), and the transmission cost (Table 1) are converted into the quadratic and linear functions of . Using definition, i.e. is derived from the using the same procedure that is derived from in Lemma 1, namely, the (4a) represented as follows [17]: (18)Consequently, variables are redefined in the form of , , where is the number of FC antennas and the number of connected sensors to FC, respectively. Using the above definitions, (11) results in (19) (20) 4 Proposed states In this section, according to the number of antennas, three states are considered for each sensor. The block diagrams in Figs. 2-4 show a collaborative WSN with energy harvesting capability, using FC multiple antennas. and denote the fundamental parameters and are estimated at time t, respectively. The proposed model's statements are summarised as follows: • The first state: Only a single antenna is placed on each sensor and all data collecting, sharing and transferring to FC, as well as harvesting and sharing energy are operated by this antenna (shown in Fig. 2). • The second state: Two antennas are placed on a sensor such that one of the antennas only transfers all data of the sensor to the FC and another antenna operates data collection from IoT, data sharing among sensors, and also energy harvesting and sharing among sensors (shown in Fig. 3). • The third state: Three antennas are placed such that data collecting from IoT and energy harvesting are operated by the first antenna, data and energy sharing are performed by the second antenna, and data transferring at the FC is operated by the third antenna (shown in Fig. 4) Fig. 2Open in figure viewerPowerPoint The diagram block of the first state at FC multiple antennas with energy harvesting and collaborative among sensors with one antenna on the sensor Fig. 3Open in figure viewerPowerPoint Diagram block of the second state at FC multiple antennas with energy harvesting and collaborative among sensors with two antennas on the sensor Fig. 4Open in figure viewerPowerPoint Diagram block of the third state at FC multiple antennas with energy harvesting and collaboration among sensor with three antennas on the sensor In the first and second states, the non-coherent transfers are used for collecting, sharing, and transferring data, because the time is not coherent for each phase of the sensor. Also, using TDMA prevents a time overlap in transmission data. Although, in the third state, each phase can be used at all times because of appropriate antennas, therefore, it is possible to use coherent MAC for this state. Note that two phases only result from data collection in the network including data collection from IoT by sensors and data collection from sensors by FC. Therefore, the data transfer rate is dependent on two phases. Moreover, a collaborative coefficient should be allocated to obtain the main solution for the problem of transmission of collected data at FC. The transferred data at FC and shared data should not be less than the collected data from IoT in order to guarantee that communication is established. Thus, the following equation is defined: (21) According to (21), the possibility of transferring the data to FC should be more than the harvested data. In case of inappropriate conditions, the following equation can be used: (22) In order to justify the limitations mentioned, more data can be transferred by the collaboration among the sensors because the received data are fixed. Thus, an optimisation problem should be considered to improve the transferred data rate using the collaborative matrix variables in collecting capacity data, or transfer capacity data to FC. Lemma 2.Both (21) and (22) are coherently established in all states. Proof.The variable can be used for having both equations simultaneously, as follows: (23)where . In (23), is determined to maximise the data rate at the FC. Therefore, this condition is considered as a constraint for the problem. We assume that and for IoT networks and sensors. Based on the conditions presented in (23), the main purpose of the problem is to maximise the data collecting in sensors. Now, in the following, the problems in the aforementioned three states are presented. • First state: Based on Table 1, including the constraints in other references, the optimisation problem for the total transferred data in the first state is obtained as follows: (24a) (24b) (24c) (24d) (24e) (24f) (24g) (24h) • Second state: In the second state, based on the number of antennas, has no effect on the amount of transfer, while the transferred data are effective in data collecting and collaborating. The optimisation problem for the second proposed state is given by (25a) (25b) (25c) (25d) (25e) (25f) • Third state: In the third state, based on the number of antennas, time distances do not affect the amount of transfer. Also, (23) is obtained as an equation in terms of SNR by simplifying the time distances in (21) and (22). With a few mathematical simplifications, we have the following optimisation problem: (26a) (26b) (26c) (26d) (26e) The difference between the third state and other previous states is related to the reduced time limitations for data collecting and energy harvesting and collaborating. The directional antennas are applicable when the channel state information (CSI) is available for each proposed states. However, the data of CSI cannot be used to direct the beam of energy antenna because the sensors are distributed randomly in a heterogeneous way in this network. Thus, the reconfigurable antenna model is more appropriate than the directed antenna model. 5 Problem optimisation It is obvious that the duration of time distances for each antenna can be effective in its optimised data rate. However, we ignore it because of the structural limitations of digital devices. Thus, all three-time distances are considered to be in the first state. In the second state, the time distance of collecting and sharing is considered to be . It is remarkable that in the third state, time distances do not have an effect on the data rate. In this section, using Lemmas 3 and 4, the necessary and sufficient conditions for convexity of all problems in three different states are studied [21]. Lemma 3.For all states, in one constraint of the optimisation problem, the data transfer rate from sensors to FC and also among collaborative sensors is versus variable. This equation is a concave function on the limitation of Proof.It is known that the logarithm is a concave function for matrices in positive matric i.e. . In the term, , the argument is always positive-definite because . Note that this function is neither concave nor convex because of the non-linear quadratic function. It is straightforward to obtain that for concavity, one has . This limitation is not restrictive because of the physical conditions of sensors for sharing and transferring data to FC. Since both equations are quadratic for SNR of collaboration and transformation at FC, they are convex functions. If the SNR is maximised, the transfer at FC increases. Hence, the optimisation problem aims to increase the collected data rate. Considering the problem for all states, the equation after some simplifications is as follows: (27a) (27b) (27c) (27d) (27e) (27f) (27g) (27h) (27i) Lemma 4.The problem is convex versus , . Proof.The problem versus , is evaluated for all states as follows: • The objective function of the problem in (26f) is considered as a scalar. • Constraint (27a) is considered such that the left side of this equation is independent of the problem optimisation variable, so it is convex. On the other hand, the right side of the equation is formed of two components. Using Lemma 3, these components are concave. If constraint (28h) is met, then the sets of the right side are also concave functions. Since the two sides of the equations are concave, this constraint is convex. • In constraint (27b), the integral of a convex function is smaller than an upper bound. Hence, it is convex. • Constraints (26c-27g) are affine inequalities versus variables, therefore, they are convex. • Constraint (28h) is established to satisfy the conditions of Lemma 3. □ Note that the storage variable of each sensor is considered as a linear function in the charging and discharging process. Therefore, it could not violate the convexity of the problem. (see the Appendix) A search Algorithm 1 (see Fig. 5) is used to find the global minimum and its corresponding , , and for these cases. For a particular number of sensor and period of the time T, the convex optimisation problem, , can be solved using an optimisation toolbox such as CVX [22] added to the MATLAB. Fig. 5Open in figure viewerPowerPoint Algorithm 1: maximisation of rate of collaborative WSN with capability of EH and WET In a normal transfer method, each sensor in a more appropriate access point from FC should be supplied with the harvested or stored energy for the significant transfer data at FC. Using the collaborative coefficients and

In this article, a new LMI method to control of discrete-time nonlinear systems based on the dissipativity theory is presented. In this approach, a nonlinear system is considered as a linear part in addition to a nonlinear term. In order to attain a quadratic bound for the nonlinear term, a sum of squares (SOS) optimization problem is solved. Dissipativity condition of the system is given using a discrete storage function and a quadratic supply rate. Consequently, a state feedback control law is obtained to ensure the system’s dissipativity. In addition, two other LMI-based optimization problems are introduced to get the maximum area domain of attraction of the nonlinear system that is a subset of the region of dissipativity. Finally, two practical nonlinear systems including a continuous stirred tank reactor (CSTR) and a quadruple-tank process are simulated to show the applicability and accuracy of the proposed dissipativity-based control approach for nonlinear systems.

A 3-D simulation of red blood cells (RBCs) described as deformable cells in plasma flow is an indispensable element of blood flow analysis in the human vessels. To numerically investigate RBC motion in shear and Poiseuille flow, a mesoscale low dimensional-RBC method based on dissipative particle dynamics method has been successfully combined with a hybrid lattice Boltzmann method-immersed boundary method. This new model decreases the computational cost compared to the low dimensional RBC method and models the deformation of red blood cell accurately. To evaluate and validate the present numerical method, the relationship between the RBC diameter and the force value derived by the low dimensional-RBC method is compared with numerical and experimental data. In addition, as a benchmark test, the deformation index as the function of the capillary number of RBC motion through a narrow cylindrical tube has been performed. The behaviour of RBC in a shear flow and Poiseuille flow has been investigated. The present results demonstrated that this model is applied to reduce the computational cost, while maintaining the model precision.

In this article, a consensus-based robust filter is proposed for sensor networks with weighted and unweighted topologies, and communication delays. The system is considered to be linear time-varying (LTV) with bounded uncertainties. In order to achieve the desired filter, first, a robust optimization problem is defined based on the consensus protocol for unweighted topologies. The consensus protocol ensures an agreement between the estimates of all sensors. By solving this problem, the proposed consensus-based robust filter is obtained and its algorithm is presented. Then, to increase the applicability of the filter, another optimization problem for weighted topologies is introduced. Next, due to the impact and high importance of communication delays in sensor networks, by considering the time-varying delays in consensus protocols, new optimization problems are solved again to achieve a suitable filter. One of the most significant features of the proposed consensus-based robust filters is that the loss of a large part of the network links does not pull down the filtering performance. Finally, in the simulation section, the robust performance and efficiency of the proposed consensus-based robust filters have been investigated for weighted and unweighted networks in the presence of time-varying delays and loss of communication links.

Summary In this study, a distributed robust moving horizon estimation (DRMHE) approach is proposed for time‐varying multisensor systems affected by stochastic and norm‐bounded uncertainties. First, by considering the uncertainties in all model matrices, stochastic min–max optimization problems in local and collective forms are presented to achieve the proposed estimator. Then, by converting the problems to robust regularized least‐squares problems with uncertain parameters, closed‐form solutions are obtained for estimations in both local and collective forms. Furthermore, the stability of the proposed estimator is investigated under some appropriate conditions. At last, two different examples are employed to show the robust performance and superiority of the proposed DRMHE approach compared to the existing methods.

Abstract This study considers a robust quadratic covariance‐constrained filtering problem for discrete time‐varying linear and non‐linear dynamic systems with non‐Gaussian noises. Non‐Gaussian noises are presumed to be unknown, bounded, and limited in a specified ellipsoidal set. In this approach, first, a general standard linear form of the filter is introduced for state estimation in linear dynamic systems. The filter gain is obtained by minimizing the upper bound of the estimation error's covariance matrix. The Lyapunov theory demonstrates the stability of this filter. Second, we extend the proposed filtering approach to non‐linear dynamic systems that are considered as a combination of linear and non‐linear terms. The Lipschitz‐like condition is assumed for the non‐linear part. A new filter structure is proposed in this case and the filter gain is obtained by the same idea to minimize the upper bound of the error's covariance matrix. Finally, four numerical examples are presented to signify the effectiveness and performance of the proposed filters for linear and non‐linear systems.

Summary In this article, a consensus‐based robust regularized least‐squares filter is designed for multi‐sensor systems with norm‐bounded uncertainties. In this approach, a min‐max optimization problem is presented based on a consensus protocol on estimates. The advantage of a consensus filter is that each node estimates its local states, in addition to reaching an agreement on estimates made by all sensors on the network. By introducing appropriate conversions the proposed optimization problem is converted to a robust regularized least‐squares problem. Solving this problem results in the structure of the proposed filter. Then, the recursive formulation of the filter is obtained in measurement form and information form. Finally, in order to investigate the efficacy, good proficiency, and robustness of the proposed consensus‐based robust least‐squares filter, it has been applied to an uncertain multi‐sensor system with 100 nodes and its results have been compared with existing consensus filters.

IET Control Theory & ApplicationsVolume 16, Issue 15 p. 1573-1585 ORIGINAL RESEARCHOpen Access Double hyperbolic sliding mode control of a three-legged robot with actuator constraints Seyyed Alireza Ghoreishi, Seyyed Alireza Ghoreishi Department of Electrical Engineering, Imam-Khomeini International University, Qazvin, IranSearch for more papers by this authorAmir Farhad Ehyaei, Corresponding Author Amir Farhad Ehyaei [email protected] orcid.org/0000-0001-5205-8966 Department of Electrical Engineering, Imam-Khomeini International University, Qazvin, Iran Correspondence Amir Farhad Ehyaei, Department of Electrical Engineering, Imam-Khomeini International University, Qazvin, Iran. Email: [email protected]Search for more papers by this authorMehdi Rahmani, Mehdi Rahmani orcid.org/0000-0002-4560-9018 Department of Electrical Engineering, Imam-Khomeini International University, Qazvin, IranSearch for more papers by this author Seyyed Alireza Ghoreishi, Seyyed Alireza Ghoreishi Department of Electrical Engineering, Imam-Khomeini International University, Qazvin, IranSearch for more papers by this authorAmir Farhad Ehyaei, Corresponding Author Amir Farhad Ehyaei [email protected] orcid.org/0000-0001-5205-8966 Department of Electrical Engineering, Imam-Khomeini International University, Qazvin, Iran Correspondence Amir Farhad Ehyaei, Department of Electrical Engineering, Imam-Khomeini International University, Qazvin, Iran. Email: [email protected]Search for more papers by this authorMehdi Rahmani, Mehdi Rahmani orcid.org/0000-0002-4560-9018 Department of Electrical Engineering, Imam-Khomeini International University, Qazvin, IranSearch for more papers by this author First published: 07 July 2022 https://doi.org/10.1049/cth2.12326AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This paper proposes an anti-wind up double hyperbolic sliding mode controller (AWDH-SMC) in the presence of torque constraints for a three-legged robot. The legged robot's dynamics are nonlinear, hybrid and complex. Based on the challenges mentioned, this study focuses on designing a sliding mode controller (SMC) for a fully actuated three-legged robot to achieve fast tracking and convergence. On the other hand, the torques generated by the actuators are limited. As a result, not only must the controller be fast so that the robot's balance is not disturbed, but it must also withstand applied torque constraints. Therefore, the double hyperbolic sliding mode controller is designed at first for fast tracking and convergence. Next, an anti-wind up compensator is used to apply torque constraints. Finally, using the theory of multiple Lyapunov functions, the stability of the closed-loop control system for the hybrid model of legged-robot is analyzed. Simulation results validate the effectiveness of the proposed control scheme. 1 INTRODUCTION The research community is interested in multi legged robotic systems because of their similarity to mammals and ability to cross various obstacles and ways [1-4]. The main challenges of these robots are balance, stability, nonlinear and hybrid dynamics, physical constraints, and control issues. More legs make the system more balanced since more points are in contact with the ground when the robot moves. However, higher number of legs increases complexity of the system; thus, making it challenging to gait design, modeling and control. This paper studies the three-legged robot to make a compromise between complexity and balance. Besides the balance problem, the main challenges for legged robots are their stability and control due to the nonlinearity of dynamics, model uncertainties and high complexity of the system [4, 5]. In this regard, several control methods, including feedback linearization control [6], robust control [7], robust adaptive control [8], neural network control [9], fuzzy control [10-12], model predictive control [13], quadratic programming nonlinear control legged robots [14] and SMC [15-18] have been applied to legged robots. The main approach used for solving balance problem in many of these methods is based on zero moment point (ZMP) [10, 11, 19]. When using the ZMP balance criterion, the robot's speed is limited, and the robot must have a flat-footed walking. The major weakness of [14] is the lack of stability proof and using the center of mass criterion for balance. Another well known strategy for balanced walking of legged robots is the Hybrid Zero Dynamics (HZD) method [20-22]. An important feature of HZD is that it turns the problem of walking stability into a problem of closed-loop stability. Therefore, HZD-based methods have two advantages. First, it is achievable to prove the stability of the closed loop system, and second, high speed walking of the robot is possible. In addition, methods based on this approach have been developed for walking on rough terrain [23], and 3D walking [24] and underactuated uneven terrain [25]. Although uneven surfaces are considered for underactuated models in [25], the general rule of control and comprehensive proof of stability is not provided. Also, the design is done without considering the constraints and limitations. On the other hand, based on the idea of HZD, analysis and proof of stability using multiple Lyapunov functions for legged robot in [26-29] are studied. The design of reference trajectory using the impact invariance method, stabilization and exponential tracking by the feedback controller for a bipedal robot is provided in [26]. The stable walking of a quadrupedal robot on a rigid dynamic surface is also given in [27]. In [28], a robust adaptive control for a bipedal robot is presented, and its hybrid stability is investigated using the theory of Lyapunov functions. Also, the motion of a bipedal robot in a straight line is examined using HZD control and its stability is proved in [29]. Most feedback controllers in the HZD method have a PD part; however, this structure is incapable of overcoming uncertainties and disturbances and has a low convergence speed. One of the advisable control methods that can overcome uncertainties and disturbances and, in addition, has a high convergence speed is the SMC. This method is prevalent due to its superior robustness, suitable transient response and simplicity [30-32]. SMC has been successfully implemented in various systems, including manipulators and legged robots [15-18, 33, 34]; however, as mentioned before, many use ZMP for balance or do not give perfect proof of stable walking. This paper uses the SMC and HZD idea combination for stable walking, and multiple Lyapunov functions investigate its stability. On the other hand, if a controller has a good performance in factors such as tracking speed, elimination of chattering and convergence, the balance and stability of the robot is more guaranteed. In this context, a lot of research has been carried out so far to improve the SMC, including second-order SMC [35], adaptive second-order terminal SMC [33], terminal SMC [36], higher order integral SMC [37], and reaching law SMC (RLSMC) [38]. Among the aforementioned schemes, RLSMC, due to its ability to decrease chattering and tracking errors, and increase the tracking speed, has been studied in [38-41]. In [38], an exponential RLSMC is presented for robotic systems to guarantee tracking performance and decrease the chattering problem . In [39], an adaptive reaching law combined with non-switching and saturated terms is introduced. The non-switching term can reduce chattering and enhance the tracking performance. In [40], an inverse hyperbolic function is used to reduce the convergence time and chattering phenomenon . A double hyperbolic sliding mode controller(DHSMC) has been presented for fast convergence and to decrease chattering in [41], and the results have been compared with other methods. The results show the superiority of double hyperbolic sliding mode control over other methods. In other words, it has the fastest convergence rate and the lowest chattering. In our last work [42], a double hyperbolic sliding mode control method based on an Unscented Kalman filter was proposed to move the body of a three-legged robot in the presence of uncertainty and noise. Fast convergence, suitable tracking and better chattering reduction compared to other methods are the advantages of the proposed method. Another challenge in legged robot control is constraints. Although some constraints are applied to reference trajectory design in HZD method, if an unwanted constraint or saturation occurs during walking, the controller must be able to handle it. Hence, the sliding mode in the presence of constraints is investigated in [43-47]. An adaptive sliding mode control scheme with control input constraint using sliding surface correction is proposed for a spacecraft system in [43]. Reducing the system's speed is one of the disadvantages of this method because the maximum amount of torque is not available. In [44], the sliding mode predictive control is used to solve the tracking problem while the constraints exist. In this method, a linear model of the system is required. An anti-wind up compensator integrated with an integral sliding mode control strategy is presented in [46] to control a linear system in the presence of constraints. In [47], robust adaptive sliding mode control with anti-wind up method is introduced for an underwater nonlinear system in the presence of constraints. The main advantages of anti-wind up compensators are using maximum torque at saturation time, and the capability to be applied in nonlinear systems. It is challenging to design a control law and prove its stability in legged robotic systems because of significant challenges such as complex mathematical modeling, balance, stability, impact during contact with the ground, different motion phases, and physical constraints. ZMP-based methods do not have a global law to guarantee stability in different phases. The HZD method suffers from a high computational complexity in achieving a direct relationship between the independent variables and inputs. On the other hand, HZD cannot overcome uncertainty and has a low convergence speed. Also, there is no global law for stability analysis for different motion phases in the conventional sliding mode control method, and it has a low convergence speed. Furthermore, none of the above methods consider the physical limitations of the controller design. Ultimately, all of this has motivated this study. In this paper, motivated by the above discussion, a new sliding mode control approach is proposed for a three-legged robot for fast tracking of the desired trajectory in the presence of torque saturation, and the closed loop stability of walking is proved using multiple Lyapunov functions. The main contributions of this paper are characterized as follows: Unlike the HZD, using the natural orthogonal complement matrix method, provides a direct relationship between control variables and input torques by a fully actuated modeling of the robot. This simplified and direct model between input and output can be used to design various control methods. Double hyperbolic sliding mode control has been proposed not only for fast convergence and chattering elimination but also for some features that aid in stability proof and do not exist in traditional sliding mode control methods. Furthermore, an anti-wind up compensator is added to the proposed method to overcome torque limitation. Anti-wind up part can apply maximum allowed torque, such that the fastest tracking is obtained. Closed-loop stability of multi-phase system with an SMC structure is proved using multiple Lyapunov functions considering the powerful features of the double hyperbolic sliding mode approach and impact invariance structure. The remainder of the paper is organized as follows: In Section 2, the robot model, including continuous dynamics and discrete impact dynamics, are introduced. In Section 3, DHSMC with explicit constraints on torques is presented. The stability of the closed-loop system is also investigated by the multiple Lyapunov functions theorem. Reference trajectory generation and simulation studies performed on a three-legged robot are provided in Sections 4 and 5, respectively. The conclusion is given in Section 6. 2 ROBOT MODEL The purpose of this work is the stable walking of a fully actuated three-legged robot. Therefore, this section introduces the hybrid model of a three-legged robot illustrated in Figure 1. FIGURE 1Open in figure viewerPowerPoint 3-legged robot model: (a) robot structure in solid works, (b) joint configuration in 3-legged robot, (c) robot base and its states The three-legged model includes continuous and discontinuous phases dynamic. Discontinuous phases are three discrete events to connect the continuous phases. If one leg is swinging, the dynamics are in a continuous phase, and when the end of the swinging leg reaches the ground, an impact is applied to the robot, which causes a jump in the robot joints [48]. In fact, the jump in the joints due to impact in the time interval between the impact of one leg with the ground, and the separation of the other leg from the ground, is a discrete phase dynamics or impact dynamics. The gait design of the robot is shown in Figure 2. FIGURE 2Open in figure viewerPowerPoint Gait design for three-legged robot As it turns out, at each continuous phase, there are a swinging leg and two legs located on the ground which can provide a better balance. The structure of the three-legged robot has 15 states. Each leg consists of three joints with generalized coordinates in the form of q L i = [ θ 1 i , θ 2 i , θ 3 i ] T $q_L^i=[\theta _1^i,\theta _2^i,\theta _3^i]^T$ , where "i" is the number of each leg as listed in Table 1. TABLE 1. Leg number Leg Location Front Left Right Leg number (i) 1 2 3 The generalized coordinates of the base are q b = [ x b , y b , z b , θ b , ϕ b , ψ b ] T $q_b=[x_b,y_b,z_b,\theta _b,\phi _b,\psi _b]^T$ . The base coordinates consist of cartesian [ x b , y b , z b ] T $[x_b,y_b,z_b]^T$ and rotational coordinates [ θ b , ϕ b , ψ b ] T $[\theta _b,\phi _b,\psi _b]^T$ . Therefore, the generalized coordinates of the robot are considered to be q = [ q L 1 , q L 2 , q L 3 , q b ] T ∈ Q $q=[q_L^1,q_L^2,q_L^3,q_b]^T \in Q$ , and Q ⊂ R n + 6 $Q \subset \mathbb {R}^{n+6}$ is the configuration space of the three-legged robot , that "n" is the number of robot joint angles. Also τ ∈ T $\tau \in {T}$ is joint torques vector, and T ⊂ R m $T \subset \mathbb {R}^{m}$ that "m" is the number of actuators. Since the number of holonomic constraints is n c = 6 $n_c = 6$ , the robot has 9 degrees of freedom [27]. On the other hand, all actuated joints of the robot are independent and as a result the robot is fully actuated. Continuous phases dynamic As mentioned earlier, in each continuous phase, one leg is swinging and two legs are on the ground. The position vector for endpoints of the fixed legs in the world frame is P s ( q ) ∈ R n c $P_s(q) \in \mathbb {R}^{n_c}$ , and to prevent the robot slipping, the holonomic constraints are expressed as follows: J s q ̇ = 0 , \begin{equation} \begin{aligned} J_s\skew4\dot{q}=0, \end{aligned} \end{equation} (1)where J s ( q ) = ∂ P s ∂ q ( q ) $J_s(q)=\frac{\partial {P_s}}{\partial {q}}(q)$ . Note that J s $J_s$ is different in each phase, since the position of the fixed legs changes. The dynamic equation of the three-legged robot is expressed as follows: M ( q ) q ̈ + C ( q , q ̇ ) q ̇ + G ( q ) = B τ + J s T F s , \begin{equation} M(q)\skew4\ddot{q}+C(q,\skew4\dot{q})\skew4\dot{q}+G(q)=B\tau +{J}_{s}^{T}{F}_{s}, \end{equation} (2)where q , q ̇ , q ̈ $q,\skew4\dot{q},\skew4\ddot{q}$ are the position, velocity and acceleration vectors, respectively. The positive matrix M ( q ) $M(q)$ is the inertia matrix, C ( q , q ̇ ) $C(q,\skew4\dot{q})$ is the Coriolis matrix, G ( q ) $G(q)$ is the gravitational vector, B is the selection matrix of actuators, and F s $F_s$ is the external force between robot and ground surface. Now, using the method of natural orthogonal complements [49], the independent equations of each phase are obtained. Assuming ν is an independent variable coordinate of the system, the velocity vector q ̇ $\skew4\dot{q}$ can be expressed based on the independent variable coordinate as follows: q ̇ = Λ ( q ) ν ̇ , \begin{equation} \begin{aligned} \skew4\dot{q}=\Lambda (q)\dot{\nu }, \end{aligned} \end{equation} (3)where Λ is natural orthogonal complement of matrix J s $J_s$ . If (3) is multiplied from the left hand by J s $J_s$ then using (1), and note that the matrix ν is an non-zero independent variable, one can write: J s Λ = 0 . \begin{equation} \begin{aligned} J_s\Lambda =0. \end{aligned} \end{equation} (4)Now, multiply (2) from the left side by Λ T $\Lambda ^T$ : Λ T M ( q ) q ̈ + Λ T C ( q , q ̇ ) q ̇ + Λ T G ( q ) = Λ T B τ + Λ T J s T F s \begin{eqnarray} &&{\mathrm{\Lambda}}^{T}M(q)\skew4\ddot{q}+{\mathrm{\Lambda}}^{T}C(q,\skew4\dot{q})\skew4\dot{q}+{\mathrm{\Lambda}}^{T}G(q)\nonumber\\ &&\quad = {\mathrm{\Lambda}}^{T}B\tau +{\mathrm{\Lambda}}^{T}{J}_{s}^{T}{F}_{s} \end{eqnarray} (5)Using (3) and its derivative q ̈ = Λ ν ̈ + Λ ̇ ν ̇ $\skew4\ddot{q}=\mathrm{\Lambda}\ddot{\nu}+\dot{\mathrm{\Lambda}}\dot{\nu}$ as well as (4), the dynamic equation (5) is rewritten as follows: Λ T M ( q ) ( Λ ν ̈ + Λ ̇ ν ̇ ) + Λ T C ( q , q ̇ ) ( Λ ( q ) ν ̇ ) + Λ T G ( q ) = Λ T B τ + ( J s Λ ) T F s \begin{align} {\mathrm{\Lambda}}^{T}M(q)(\mathrm{\Lambda}\ddot{\nu}+\dot{\mathrm{\Lambda}}\dot{\nu})+& {\mathrm{\Lambda}}^{T}C(q,\skew4\dot{q})(\mathrm{\Lambda}(q)\dot{\nu})\nonumber\\ +& {\mathrm{\Lambda}}^{T}G(q)={\mathrm{\Lambda}}^{T}B\tau +{({J}_{s}\mathrm{\Lambda})}^{T}{F}_{s} \end{align} (6)Finally, the equation of independent variables is obtained as follows: M ¯ i ν ̈ + C ¯ i ν ̇ + G ¯ i = B ¯ i τ \begin{align} {\bar{M}}_{i}\ddot{\nu}+{\bar{C}}_{i}\dot{\nu}+{\bar{G}}_{i}={\bar{B}}_{i}\tau \end{align} (7)where M ¯ i = Λ T M Λ $\bar{M}_i=\Lambda ^TM\Lambda$ , C ¯ i = Λ T ( M Λ ̇ + C Λ ) $\bar{C}_i=\Lambda ^T(M\dot{\Lambda }+C\Lambda )$ , G ¯ i = Λ T G $\bar{G}_i=\Lambda ^TG$ , B ¯ i = Λ T B $\bar{B}_i=\Lambda ^TB$ and i = 1 , 2 , 3 $i=1,2,3$ is the number of each phase. Now to calculate Λ, without loss of generality, we suppose that legs 1 and 3 are on the ground. Now, (1) can be rewritten as follows: ∂ P s 1 ∂ q q ̇ = ∂ P s 1 ∂ q ( 1 ) q ̇ ( 1 ) + ∂ P s 1 ∂ q ( 2 ) q ̇ ( 2 ) + ∂ P s 1 ∂ q ( 3 ) q ̇ ( 3 ) + ∂ P s 1 ∂ q ( 10 ) q ̇ ( 10 ) + ∂ P s 1 ∂ q ( 11 ) q ̇ ( 11 ) + ∂ P s 1 ∂ q ( 12 ) q ̇ ( 12 ) + ∂ P s 1 ∂ q ( 13 ) q ̇ ( 13 ) + ∂ P s 1 ∂ q ( 14 ) q ̇ ( 14 ) + ∂ P s 1 ∂ q ( 15 ) q ̇ ( 15 ) = 0 \begin{align} \def\eqcellsep{&}\begin{array}{rcl} \displaystyle\frac{\partial {P}_{s}^{1}}{\partial q}\skew4\dot{q}& =& \displaystyle\frac{\partial {P}_{s}^{1}}{\partial q(1)}\skew4\dot{q}(1)+\frac{\partial {P}_{s}^{1}}{\partial q(2)}\skew4\dot{q}(2)+\frac{\partial {P}_{s}^{1}}{\partial q(3)}\skew4\dot{q}(3)\\[12pt] && +\; \displaystyle\frac{\partial {P}_{s}^{1}}{\partial q(10)}\skew4\dot{q}(10)+\frac{\partial {P}_{s}^{1}}{\partial q(11)}\skew4\dot{q}(11)+\frac{\partial {P}_{s}^{1}}{\partial q(12)}\skew4\dot{q}(12)\\[12pt] && +\; \displaystyle\frac{\partial {P}_{s}^{1}}{\partial q(13)}\skew4\dot{q}(13)+\frac{\partial {P}_{s}^{1}}{\partial q(14)}\skew4\dot{q}(14)+\frac{\partial {P}_{s}^{1}}{\partial q(15)}\skew4\dot{q}(15)=0\end{array} \end{align} (8) ∂ P s 3 ∂ q q ̇ = ∂ P s 3 ∂ q ( 7 ) q ̇ ( 7 ) + ∂ P s 3 ∂ q ( 8 ) q ̇ ( 8 ) + ∂ P s 3 ∂ q ( 9 ) q ̇ ( 9 ) + ∂ P s 3 ∂ q ( 10 ) q ̇ ( 10 ) + ∂ P s 3 ∂ q ( 11 ) q ̇ ( 11 ) + ∂ P s 3 ∂ q ( 12 ) q ̇ ( 12 ) + ∂ P s 3 ∂ q ( 13 ) q ̇ ( 13 ) + ∂ P s 3 ∂ q ( 14 ) q ̇ ( 14 ) + ∂ P s 3 ∂ q ( 15 ) q ̇ ( 15 ) = 0 \begin{eqnarray} \frac{\partial {P}_{s}^{3}}{\partial q}\skew4\dot{q}& =& \frac{\partial {P}_{s}^{3}}{\partial q(7)}\skew4\dot{q}(7)+\frac{\partial {P}_{s}^{3}}{\partial q(8)}\skew4\dot{q}(8)+\frac{\partial {P}_{s}^{3}}{\partial q(9)}\skew4\dot{q}(9)\nonumber\\[4pt] && +\;\frac{\partial {P}_{s}^{3}}{\partial q(10)}\skew4\dot{q}(10)+\frac{\partial {P}_{s}^{3}}{\partial q(11)}\skew4\dot{q}(11)+\frac{\partial {P}_{s}^{3}}{\partial q(12)}\skew4\dot{q}(12)\nonumber\\[4pt] && +\; \frac{\partial {P}_{s}^{3}}{\partial q(13)}\skew4\dot{q}(13)+\frac{\partial {P}_{s}^{3}}{\partial q(14)}\skew4\dot{q}(14)+\frac{\partial {P}_{s}^{3}}{\partial q(15)}\skew4\dot{q}(15)=0\nonumber\\ \end{eqnarray} (9)where q ( k ) $q(k)$ is the kth element on the vector q, and P s j $P_s^j$ is the position vector of endpoint to the leg with number j in world frame. Using equations (8) and (9), we have: q ̇ ( 10 ) q ̇ ( 11 ) ⋮ q ̇ ( 15 ) = − ∂ P s 1 ∂ q ( 10 ) ∂ P s 1 ∂ q ( 11 ) ⋯ ∂ P s 1 ∂ q ( 15 ) ∂ P s 3 ∂ q ( 10 ) ∂ P s 3 ∂ q ( 11 ) ⋯ ∂ P s 3 ∂ q ( 15 ) − 1 × ∂ P s 1 ∂ q ( 1 ) ∂ P s 1 ∂ q ( 2 ) ∂ P s 1 ∂ q ( 3 ) 0 3 * 1 0 3 * 1 0 3 * 1 0 3 * 1 0 3 * 1 0 3 * 1 ∂ P s 3 ∂ q ( 7 ) ∂ P s 3 ∂ q ( 8 ) ∂ P s 3 ∂ q ( 9 ) q ̇ ( 1 ) q ̇ ( 2 ) q ̇ ( 3 ) q ̇ ( 7 ) q ̇ ( 8 ) q ̇ ( 9 ) \begin{align} \def\eqcellsep{&}\begin{array}{ll} \left( \def\eqcellsep{&}\begin{array}{c}\skew4\dot{q}(10)\\[3pt] \skew4\dot{q}(11)\\[3pt] \vdots \\[3pt] \skew4\dot{q}(15)\end{array} \right)=-{\left( \def\eqcellsep{&}\begin{array}{ccc} \dfrac{\partial {P}_{s}^{1}}{\partial q(10)}& \dfrac{\partial {P}_{s}^{1}}{\partial q(11)}& \dots \dfrac{\partial {P}_{s}^{1}}{\partial q(15)}\\[12pt] \dfrac{\partial {P}_{s}^{3}}{\partial q(10)}& \dfrac{\partial {P}_{s}^{3}}{\partial q(11)}& \dots \dfrac{\partial {P}_{s}^{3}}{\partial q(15)}\end{array} \right)}^{-1}& \\[3pt] \times \;\left( \def\eqcellsep{&}\begin{array}{cccccc} \dfrac{\partial {P}_{s}^{1}}{\partial q(1)}& \dfrac{\partial {P}_{s}^{1}}{\partial q(2)}& \dfrac{\partial {P}_{s}^{1}}{\partial q(3)}& {0}_{3\ast 1}& {0}_{3\ast 1}& {0}_{3\ast 1} \\[12pt] {0}_{3\ast 1}& {0}_{3\ast 1}& {0}_{3\ast 1}& \dfrac{\partial {P}_{s}^{3}}{\partial q(7)}& \dfrac{\partial {P}_{s}^{3}}{\partial q(8)}& \dfrac{\partial {P}_{s}^{3}}{\partial q(9)} \end{array} \right)& \left( \def\eqcellsep{&}\begin{array}{c} \skew4\dot{q}(1)\\[3pt] \skew4\dot{q}(2)\\[4pt] \skew4\dot{q}(3)\\[4pt] \skew4\dot{q}(7)\\[4pt] \skew4\dot{q}(8)\\[4pt] \skew4\dot{q}(9)\end{array} \right)\end{array} \nonumber\\ \end{align} (10) q ̇ ( 10 : 15 ) = Γ 1 * q ̇ ( 1 : 3 ) q ̇ ( 7 : 9 ) = Γ 12 Γ 22 q ̇ ( 1 : 3 ) q ̇ ( 7 : 9 ) \begin{equation} \skew4\dot{q}(10:15)={\mathrm{\Gamma}}_{1}\ast \left( \def\eqcellsep{&}\begin{array}{c}\skew4\dot{q}(1:3)\\ \skew4\dot{q}(7:9)\end{array} \right)=\left( \def\eqcellsep{&}\begin{array}{cc}{\mathrm{\Gamma}}_{12}& {\mathrm{\Gamma}}_{22}\end{array} \right)\left( \def\eqcellsep{&}\begin{array}{c}\skew4\dot{q}(1:3)\\ \skew4\dot{q}(7:9)\end{array} \right) \end{equation} (11)If the independent variables are selected as ν = q ̇ ( 1 : 9 ) $\nu =\skew4\dot{q}(1:9)$ , then using (11), it can be concluded that: q ̇ ( 1 : 3 ) q ̇ ( 4 : 6 ) q ̇ ( 7 : 9 ) q ̇ ( 10 : 15 ) = I 3 * 3 0 3 * 3 0 3 * 3 0 3 * 3 I 3 * 3 0 3 * 3 0 3 * 3 0 3 * 3 I 3 * 3 Γ 12 0 6 * 3 Γ 22 q ̇ ( 1 : 3 ) q ̇ ( 4 : 6 ) q ̇ ( 7 : 9 ) \begin{equation} \left( \def\eqcellsep{&}\begin{array}{c}\skew4\dot{q}(1:3)\\[4pt] \skew4\dot{q}(4:6)\\[4pt] \skew4\dot{q}(7:9)\\[4pt] \skew4\dot{q}(10:15)\end{array} \right)=\left( \def\eqcellsep{&}\begin{array}{ccc}{I}_{3\ast 3}& {0}_{3\ast 3}& {0}_{3\ast 3}\\[4pt] {0}_{3\ast 3}& {I}_{3\ast 3}& {0}_{3\ast 3}\\[4pt] {0}_{3\ast 3}& {0}_{3\ast 3}& {I}_{3\ast 3}\\[4pt] {\mathrm{\Gamma}}_{12}& {0}_{6\ast 3}& {\mathrm{\Gamma}}_{22}\end{array} \right)\left( \def\eqcellsep{&}\begin{array}{c}\skew4\dot{q}(1:3)\\[4pt] \skew4\dot{q}(4:6)\\[4pt] \skew4\dot{q}(7:9)\end{array} \right) \end{equation} (12)where Λ 1 = I 3 * 3 0 3 * 3 0 3 * 3 0 3 * 3 I 3 * 3 0 3 * 3 0 3 * 3 0 3 * 3 I 3 * 3 Γ 12 0 6 * 3 Γ 22 \begin{equation*} {\mathrm{\Lambda}}_{1}=\left( \def\eqcellsep{&}\begin{array}{ccc}{I}_{3\ast 3}& {0}_{3\ast 3}& {0}_{3\ast 3}\\ {0}_{3\ast 3}& {I}_{3\ast 3}& {0}_{3\ast 3}\\ {0}_{3\ast 3}& {0}_{3\ast 3}& {I}_{3\ast 3}\\ {\mathrm{\Gamma}}_{12}& {0}_{6\ast 3}& {\mathrm{\Gamma}}_{22}\end{array} \right) \end{equation*} is natural orthogonal complement for this case. Considering B = I 3 * 3 0 3 * 3 0 3 * 3 0 3 * 3 I 3 * 3 0 3 * 3 0 3 * 3 0 3 * 3 I 3 * 3 0 6 * 3 0 6 * 3 0 6 * 3 \begin{equation*} B=\left( \def\eqcellsep{&}\begin{array}{ccc}{I}_{3\ast 3}& {0}_{3\ast 3}& {0}_{3\ast 3}\\ {0}_{3\ast 3}& {I}_{3\ast 3}& {0}_{3\ast 3}\\ {0}_{3\ast 3}& {0}_{3\ast 3}& {I}_{3\ast 3}\\ {0}_{6\ast 3}& {0}_{6\ast 3}& {0}_{6\ast 3}\end{array} \right) \end{equation*} matrix B ¯ 1 $\bar{B}_1$ is obtained as follows: B ¯ 1 = Λ 1 T * B = I 3 * 3 0 3 * 3 0 3 * 3 Γ 12 T 0 3 * 3 I 3 * 3 0 3 * 3 0 3 * 6 0 3 * 3 0 3 * 3 I 3 * 3 Γ 22 T * I 3 * 3 0 3 * 3 0 3 * 3 0 3 * 3 I 3 * 3 0 3 * 3 0 3 * 3 0 3 * 3 I 3 * 3 0 6 * 3 0 6 * 3 0 6 * 3 = I 9 * 9 \begin{align} {\bar{B}}_{1}& ={\mathrm{\Lambda}}_{1}^{T}\ast B\nonumber\\ & =\left( \def\eqcellsep{&}\begin{array}{cccc}{I}_{3\ast 3}& {0}_{3\ast 3}& {0}_{3\ast 3}& {\mathrm{\Gamma}}_{12}^{T}\\ {0}_{3\ast 3}& {I}_{3\ast 3}& {0}_{3\ast 3}& {0}_{3\ast 6}\\ {0}_{3\ast 3}& {0}_{3\ast 3}& {I}_{3\ast 3}& {\mathrm{\Gamma}}_{22}^{T}\end{array} \right)\ast \left( \def\eqcellsep{&}\begin{array}{ccc}{I}_{3\ast 3}& {0}_{3\ast 3}& {0}_{3\ast 3}\\ {0}_{3\ast 3}& {I}_{3\ast 3}& {0}_{3\ast 3}\\ {0}_{3\ast 3}& {0}_{3\ast 3}& {I}_{3\ast 3}\\ {0}_{6\ast 3}& {0}_{6\ast 3}& {0}_{6\ast 3}\end{array} \right)\nonumber\\ & ={I}_{9\ast 9} \end{align} (13)In the same way, B ¯ i = I 9 ∗ 9 $\bar{B}_i=I_{9*9}$ , for all i, and (7) is expressed as: M ¯ i ν ̈ + C ¯ i ν ̇ + G ¯ i = τ \begin{align} {\bar{M}}_{i}\ddot{\nu}+{\bar{C}}_{i}\dot{\nu}+{\bar{G}}_{i}=\tau \end{align} (14)This equation creates a direct relationship between the independent variables and the torques. Discontinuous phases dynamic When the swinging leg hits the ground, it causes a jump in q ̇ $\skew4\dot{q}$ , but q does not change suddenly as a result of the impact. This event causes a continuous and discrete phase connection. The switching surface S s l ( q , q ̇ ) $S_{sl}(q,\skew4\dot{q})$ due to this event is defined as follows: S sl ( q , q ̇ ) : = { ( q , q ̇ ) ∈ TQ : α sl ( q ) = 0 , d α sl dq q ̇ < 0 } \begin{align} {S}_{\textit{sl}}(q,\skew4\dot{q}):=\{(q,\skew4\dot{q})\in \textit{TQ}:{\alpha}_{\textit{sl}}(q)=0,\frac{d{\alpha}_{\textit{sl}}}{\textit{dq}}\skew4\dot{q}<0\} \end{align} (15)where T Q $TQ$ is tangent space of Q, and α s l ( q ) $\alpha _{sl}(q)$ is the shortest distance from the swing leg to the ground. Continuous dynamics (2) and holonomic constraints (1) due to the impact are modified to: M ( q ̇ + − q ̇ − ) = J s T δ F s \begin{align} M({\skew4\dot{q}}^{+}-{\skew4\dot{q}}^{-})={J}_{s}^{T}\delta {F}_{s} \end{align} (16) J s q ̇ + = 0 \begin{align} {J}_{s}{\skew4\dot{q}}^{+}=0 \end{align} (17)where superscripts + and − shows the value of parameter immediately after and before the impact, respectively, and δ F s $\delta F_s$ is the impulsive force due to impact. Using (16) and (17), δ F s $\delta F_s$ is achieved as follows: δ F s = − ( J s M − 1 J s T ) − 1 J s q ̇ − \begin{align} \delta {F}_{s}=-{({J}_{s}{M}^{-1}{J}_{s}^{T})}^{-1}{J}_{s}{\skew4\dot{q}}^{-} \e

Optimal control of large-scale uncertain dynamic systems with time delays in states is considered in this paper. For this purpose, a two-level strategy is proposed to decompose the large-scale system into several interconnected subsystems at the first level. Then optimal control inputs are obtained by minimization of convex performance indices in presence of uncertainties, in the form of states and interactions feedback. The solution is achieved by bounded data uncertainty problems, where the uncertainties are only needed to be bounded and it is not required to satisfy the so-called ‘matching conditions’. At the second level, a simple substitution-type interaction prediction method is used to update the interaction parameters between subsystems. An iterative two-level algorithm is proposed to coordinate their solutions and achieve the optimal solution of the overall large-scale system. Applicability and performance of the proposed algorithm is shown through simulation of a two coupled inverted pendulums.

We present design and construction of a large low-mass Triple-GEM detector prototype for forward tracking at a future Electron-Ion Collider. In this environment, multiple scattering of forward and backward tracks must be minimized so that electron tracks can be cleanly matched to calorimeter clusters and so that hadron tracks can efficiently seed RICH ring reconstruction for particle identification. Consequently, the material budget for the forward tracking detectors is critical. The construction of the detector builds on the mechanical foil stretching and assembly technique pioneered by CMS for the muon endcap GEM upgrade. As an innovation, this detector implements drift and readout electrodes on thin large foils instead of on PCBs. These foils get stretched mechanically together with three GEM foils in a single stack. This reduces the radiation length of the total detector material in the active area by a factor seven from over 4% to below 0.6%. It also aims at improving the uniformity of drift and induction gap sizes across the detector and consequently signal response uniformity. Thin outer frames custom-made from carbon-fiber composite material take up the tension from the stretched foil stack and provide detector rigidity while keeping the detector mass low. The gas volume is closed with thin aluminized polyimide foils. The trapezoidal detector covers an azimuthal angle of 30.1 degrees and a radius from 8 cm to 90 cm. It is read out with radial zigzag strips with pitches of 1.37 mrad at the outer radius and 4.14 mrad at the inner radius that reduce the number of required electronics channels and associated cost while maintaining good spatial resolution. All front-end readout electronics is located away from the active area at the outer radius of the trapezoid. Scans of small readout boards with the same type of zigzag strip structure using highly collimated X-rays show spatial resolutions of 60-90 microns.

Choosing an appropriate local optimal region in order to satisfy the location priorities and to guarantee enough robustness against measurement biases is desired in many optimization problems. To fulfill such aim, all locally convex regions which potentially contain optimal points must be approximated. In this paper, using a quadratic-based fuzzy clustering, approximation of locally convex regions of Multiple-Convex Functions (MCFs) is intended. At first, using an incremental fuzzy clustering approach, the input space is partitioned as hyper-rectangle regions in which Locally Quadratic Models (LQMs) are identified. Based on the Hessian matrices of LQMs, some clusters, that potentially contain convex regions, are chosen. Around a certain patch of each chosen cluster, a high-order model is fitted, through which a Gradient-based Ordinal Differential Equation (GODE) is defined. Estimating the domain of attraction of each defined GODE, a locally convex region is approximated. Then, robustness of the approximated convex regions, against unknown bounded biases of input variables, is discussed. A theorem is stated which conservatively determines the sub-regions remaining convex even in presence of the uncertainty. To explain the methodology of the proposed method, an illustrative example is given. Then, the suggested method is applied to the power economic dispatch (PED) problem. The achieved results demonstrate the capability of the proposed method.

Automated ranking of pre-trained Deep Neural Networks (DNNs) reduces the required time for selecting optimal pre-trained DNN and boost the classification performance in transfer learning. In this paper, we introduce a novel algorithm to rank pre-trained DNNs by applying a straightforward distance-based complexity measure named Separation Index (SI) to the target dataset. For this purpose, at first, a background about the SI is given and then the automated ranking algorithm is explained. In this algorithm, the SI is computed for the target dataset which passes from the feature extracting parts of pre-trained DNNs. Then, by descending sort of the computed SIs, the pre-trained DNNs are ranked, easily. In this ranking method, the best DNN makes maximum SI on the target dataset and a few pre-trained DNNs may be rejected in the case of their sufficiently low computed SIs. The efficiency of the proposed algorithm is evaluated by using three challenging datasets including Linnaeus 5, Breast Cancer Images, and COVID-CT. For the two first case studies, the results of the proposed algorithm exactly match with the ranking of the trained DNNs by the accuracy on the target dataset. For the third case study, despite using different preprocessing on the target data, the ranking of the algorithm has a high correlation with the ranking resulted from classification accuracy.

Reliability is an essential factor in Photovoltaic (PV) systems. Solar power has become one of the most popular renewable power resources in recent years. Solar power has drawn attention because it is free and almost available worldwide. Moreover, the price of maintenance is lower than other power resources. Since there are no moving parts in PV systems, their reliability is relatively high. It is assumed that a typical PV system can operate 20–25 years with minimum possible interruptions. However, solar power systems may fail, the same as any other systems. It is indicated by several studies that the PV inverters are responsible for major failures in PV systems, as other components are almost passive. Hence, the reliability of the inverter has maximum impact on the reliability of the whole PV system. Thus, not only assessing and calculating the reliability value of inverter is highly crucial, but also increasing its value is essential, as well. This paper calculates and evaluates the reliability of PV single-stage inverters exclusively. Furthermore, there are suggestions that improve their reliability value.

This paper investigates the L p filtering problem for linear dynamic systems. The main objective is to discuss the optimal filter for non-Gaussian systems. The filter structure is obtained by extension of the maximum a posteriori estimation problem for general norm exponential probability density functions. The obtained filter has a linear structure, and two different algorithms are proposed for 1 ≤ p < ∞ and p = ∞ . In the following, the choice of p has been discussed based on the asymptotic distribution and the central limit theorem as well as the kurtosis of error probability density function. Both of them confirm that the L 2 filter is optimal for Gaussian systems, and the L p filter, for p < 2 , has the best performance for the systems with leptokurtic error distributions, and for p > 2 , it is the best for the systems with platykurtic error distributions. In this regard, it is shown that the L 1 and L ∞ filters have the best MSE performance for the systems with Laplacian and uniform error probability distribution functions, respectively. Simulation results verify the superior performance of the proposed filtering approach for linear time-invariant and time-varying systems.

The possibility of producing a measurable long-lived dark Z boson, that is assumed to mix kinetically with the hypercharge gauge boson in Higgs decays and to be produced also in Higgs decays through Higgs-to-dark-Higgs mixing, at the Large Hadron Collider (LHC) is investigated.Displaced dimuons in the final state are considered where each of the Z and the dark Z bosons decays directly to a dimuon.The total cross sections for the decay modes of interest as well as the decay widths and decay lengths are calculated to next-to-leading order (NLO) by using Monte Carlo (MC) simulation in the framework of M G 5_aMC@NLO and compared to the available analytical calculations to leading order (LO).The sensitivity of the LHC in Runs 2 and 3 to such searches is discussed.

Κατά τη διάρκεια των τριών τελευταίων περιόδων του run του πειράματος ΝΑ14/2 της φωτοπαραγωγής σωματιδίων με κβαντικό αριθμό charm, έχουν συλλεχθεί περίπου 4.5 εκατομμύρια γεγονότα. Τα γεγονότα αυτά όταν αναλυθούν με την προσθήκη της πληροφορίας που δίνεται από το δεύτερο Cerenkov, έχουν ένα διευρυμένο εύρος αναγνώρισης σωματιδίων στην περιοχή χαμηλών όρμων. Ερευνούνται οι ιδιότητες και τα χαρακτηριστικά παραγωγής των Λc βαρυονίων, που βρέθηκαν από τα τελικά επιλεγμένα γεγονότα. Μια σύντομη θεωρητική εισαγωγή περιγράφει τη φυσική charm και τα πρότυπα φωτοπαραγωγής. Περιγράφονται η παραγωγή της τελικής δέσμης φωτονίων υψηλής ενέργειας &lt;Εγ&gt; ≈100 GeV και η διάταξη και κατασκευή των συσκευών και ανιχνευτών και κρίνονται οι τεχνικές ιδιότητες και δυσκολίες που αντιμετωπίσθηκαν. Η ανάλυση των δεδομένων επικεντρώθηκε στο δεύτερο απαριθμητή Cerenkov, που σχεδιάστηκε και κατασκευάστηκε στο Eθνικό Μετσόβιο Πολυτεχνείο, έτσι δόθηκε ιδιαίτερη έμφαση στην περιγραφή του απαριθμητή αυτού. Δίνεται μια σύντομη περιγραφή των τηλεσκοπίων πυριτίου, όσον αφορά τον εντοπισμό χαρακτηριστικής τοπολογίας charm (charm pattern recognition) και την ανακατασκευή των κορυφών. Σύντομη περιγραφή δίνεται για την επιλογή των δεδομένων, την ανακατασκευή των τροχιών και κορυφών, την αναγνώριση των σωματιδίων, τόσο των charm όσο και των υπολοίπων σωματιδιων. Η μέτρηση της ενεργού μάζας, του χρόνου ζωής και της ασυμμετρίας του Λc δίνονται ως εξής: Mass of Λc ≈ (2.286 ± 0.002) GeV, Lifetime, τΛc ≈ (0.174 +0.078 -0.052) ps Λc/Λc ≈ 0.7 ± 0.5. Τα αποτελέσματα της ανάλυσης για το Λc της διατριβής αυτής βρίσκονται σε συμφωνία με αποτελέσματα από άλλα πειράματα φωτοπαραγωγής.

In this work, two simple approaches have been introduced to predict heat of detonation of highenergetic materials. Experimental heat of detonation of 74 energetic compounds were collected from articles and this data set was separated randomly into two groups, i.e., training and prediction sets, which were used for generation and evaluation of suitable models. Multiple linear regression (MLR) analysis was employed to build a linear model, while nonlinear models were developed by means of an artificial neural network (ANN). The obtained models with four descriptors involved show good predictive power for the test set: a squared correlation coefficient (R2) of 0.798 and a standard error (SE) of estimation of 606.48 (J/g) were achieved by the MLR model; whereas by the ANN model, R2 and SE were 0.98 and 189.4 (J/g), respectively. On the basis of the large R2 value and small SE values, one can deduce that the predicted results are in good agreement with the measured values.

Theory-based law by German and French authors (Kahn and Bartyn) was introduced in 1980. This theory was ac- cepted by the British courts. According to this theory, the initial trial of the case in accordance with its domestic law, examines the relationship factors. Original jurisdiction means the jurisdiction of the courts of the place of residence is dealt with in ¬ rights and international law as a principle has been accepted. Headquartered jurisdiction in cases such as those described in relation ¬, ¬ bunch of non-related subject of dispute with one of the association and civil liability also applies in some cases. The procedure, how to reason and how to convey notification to collect the sum and ¬ securities law is consistent with the provisions of the court in these cases, the Hague Conven- tion on jurisdiction of the Court endorsed the headquarters. Relational system of private international law to determine the applicable law provides that the court may judge that ¬ can be divided into two categories: (1) factors related to the contract, and (2) factors related parties. Factors associated with the contract are fulfilled location, location, contract signing and the closest connection. Factors related parties are as follows: residence, place of residence and place of business. This paper examines the question of the jurisdiction of that court ¬ to Where and in what cases the courts are bound to enforce their own domestic law irrespective of foreign law say? tion. Article 971 of the Civil Code involving rules of international jurisdiction has decreed: Claims Courts and the Law on Pro- cedure in terms of the local law where the action will be. Being raised in the dispute resolver foreign court of competent Iranian courts would not. Therefore, in accordance with the rules of court fights have been raised with respect to the determination of jurisdiction under the Act is made . However, in view of the specific provisions of the law of the jurisdiction of international courts has been predicted to have the rules of domestic jurisdic- tion, so will use in terms of fact In France too, rules regarding the qualification of international lack of internal jurisdiction rules of the usually resorting to analogical to determine the in- ternational jurisdiction has also been extended. The Iranian judge to determine the competency of international jurisdiction to rule on the law of civil procedure is expected to be presented. The provisions of Articles 11 to 25 of the Civil Procedure Code is mentioned.

Heats of explosion of 69 double base propellants and 62 composite modified double base (CMDB) propellants with different compositions were measured experimentally. These data and the measured values from the other references were used for the evaluation of heats of explosion of different types of energetic materials. Artificial neural network (ANN) and multiple linear regression (MLR) models were developed for this purpose. Two series of data containing 90 and 78 data were applied for modeling of double base and CMDB propellants, respectively. Each series was separated randomly into two groups, training and prediction sets, respectively, which were used for generation and evaluation of suitable models. The predicted results of ANN and MLR models were more reliable than those obtained by mass percentages and heats of explosion of individual components.

In this research, the effect of waste ground rubber tire (WGRT) powder was experimentally investigated on mechanical properties of polypropylene (PP). PP-g-MA compatibilizer was used to increase the compatibility of waste rubber tire powder with the PP matrix. All the samples were mixed in a co-rotating twin screw extruder and were formed into standard tensile and impact bars using the injection molding method. The morphology of combinations was studied by field emission scanning electron microscopy (FESEM). The FESEM micrographs taken from fracture surface of the parts indicated that PP-g-MA led to compatibility increase of tire powder with the PP matrix and better dispersion and prevented from agglomeration of tire powder in that. Adding tire powder to PP matrix in all binary and ternary combinations increased impact strength of PP. In the blends containing 5 wt% PP-g-MA, significant changes in tensile properties of the compositions occurred that may be caused by the created appropriate bond strength in this weight percent of PP-g-MA between tire powder particles and PP matrix. Young's modulus, yield stress and tensile strength of ternary combinations increased by the decrease of the weight percent of tire powder and increase of PP-g-MA, which were attributed to the increased bond strength. Also, break elongation decreased with the decrease of the weight percent of tire powder and increase of the amount of PP-g-MA, due to the reduced soft rubber phase and increased bond strength.

We present design and construction of a large low-mass Triple-GEM detector prototype for forward tracking at a future Electron-Ion Collider. In this environment, multiple scattering of forward and backward tracks must be minimized so that electron tracks can be cleanly matched to calorimeter clusters and so that hadron tracks can efficiently seed RICH ring reconstruction for particle identification. Consequently, the material budget for the forward tracking detectors is critical. The construction of the detector builds on the mechanical foil stretching and assembly technique pioneered by CMS for the muon endcap GEM upgrade. As an innovation, this detector implements drift and readout electrodes on thin large foils instead of on PCBs. These foils get stretched mechanically together with three GEM foils in a single stack. This reduces the radiation length of the total detector material in the active area by a factor seven from over 4% to below 0.6%. It also aims at improving the uniformity of drift and induction gap sizes across the detector and consequently signal response uniformity. Thin outer frames custom-made from carbon-fiber composite material take up the tension from the stretched foil stack and provide detector rigidity while keeping the detector mass low. The gas volume is closed with thin aluminized polyimide foils. The trapezoidal detector covers an azimuthal angle of 30.1 degrees and a radius from 8 cm to 90 cm. It is read out with radial zigzag strips with pitches of 1.37 mrad at the outer radius and 4.14 mrad at the inner radius that reduce the number of required electronics channels and associated cost while maintaining good spatial resolution. All front-end readout electronics is located away from the active area at the outer radius of the trapezoid.

This paper presents a novel method to design a robust L1 observer and its circuit implementation for the problems of fault diagnosis and state estimation in nonlinear systems expressed by Takagi–Sugeno models. The proposed observer is able to estimate states of system, process/actuator and sensor faults at the same time, and also has a high resistance to disturbances. The sufficient conditions to design the proposed observer such that ensuring the stability of the system based on to the Lyapunov theory and minimising an L1 performance index are given by Linear Matrix Inequality (LMI) optimisation problems. Moreover, the circuit implementation of the Van der Pol system and the proposed observer scheme is provided in detail. Also, the simulation results validate the effectiveness of the proposed L1 observer and fault diagnosis approach.

A distributed robust error-constrained filter is proposed for time-varying uncertain systems with non-Gaussian noises over a sensor network. In this problem, some challenges are raised. The distributed filter should be designed for a sensor network with uncertain parameters that are supposed to belong to a polytope with known vertices, and the non-Gaussian noises that are unknown but bounded by a set of specific ellipsoids. According to the network topology, available measurements at each sensor node came not only from the individual sensor but also from its neighbours. In this approach, to consider the effects of the neighbouring node's estimation and output in the filtering algorithm, first, a distributed filter structure is introduced at each node. Then, a collective model of the sensor network is presented with the aim of distributed filtering. Next, a linear matrix inequality-based optimisation problem is presented to guarantee the optimal performance of filtering by minimising the upper bound of the estimation error in the presence of non-Gaussian bounded noises and polytopic uncertainty. The proposed distributed approach can be easily applied as a decentralised robust error-constrained filter. In the end, two illustrative examples are presented to show the applicability and performance of the proposed error-constrained filtering approach.

This paper introduces a two-level robust approach to estimate the unknown states of a large-scale power system while the measurements and network parameters are subjected to uncertainties. The bounded data uncertainty (BDU) considered in the power network is a structured uncertainty which is inevitable in practical systems due to error in transmission lines, inaccurate modelling, unmodeled dynamics, parameter variations, and other various reasons. In the proposed approach, the corresponding network is first decomposed into smaller subsystems (areas), and then a two-level algorithm is presented for state estimation. In this algorithm, at the first level, each area uses a weighted least squares (WLS) technique to estimate its own states based on a robust hybrid estimation utilizing phasor measurement units (PMUs), and at the second level, the central coordinator processes all the results from the subareas and gives a robust estimation of the entire system. The simulation results for IEEE 30-bus test system verifies the accuracy and performance of the proposed multi-area robust estimator.

Teacher Form of Psychological Pathology for Adoloscents: Preliminary Study of Development and Psychomentric Properties

An analysis of the privacy statement of the public libraries and providing a privacy statement for public libraries in Iran

Purpose and background: Organizational commitment in management and behavioral science literature is an important factor in the relationships between organizations and individuals. The purpose of this research is to identify and evaluate the organizational commitment of librarians in libraries in Tehran based on 4 indicators of participation and teamwork spirit, conscientiousness, values, and administrative discipline. Financial and social took place. Research method: The current research was applied in terms of purpose and survey research in terms of method. In the present study, data were collected using standard questionnaires and interviews. The statistical population included all librarians of academic and public libraries in Tehran, numbering 780 people. In this research, using Cochran's formula, 257 people were selected as a sample population. Also, the snowball technique was used in the interview method to collect data. Findings: The results of the research showed that the public participation component is the most important component in the discussion of the organizational commitment of librarians in libraries in Tehran. And the components of central justice and responsibility are in the next ranks. Also, the results showed that the librarians of Iranian libraries are in the first rank in the index of participation and group spirit, the index of work conscience is in the second rank, and the index of administrative, financial and social discipline is in the rank of The third and the index of values are in the fourth place. Also, the results of the research showed that the level of adherence to organizational commitment in academic libraries and public libraries is not significantly different, but the condition of university library employees is slightly better than public library employees. Conclusion: It goes without saying that the ultimate goal of performance evaluation in any field is the exchange of information between the evaluator and the employees in order to prevent and correct undesirable performance and encourage the desired performance of employees. For this purpose, care should be taken during the evaluation session to move towards the conclusion of the topics.

Background and purpose: With the advancement of science and the increase of electronic resources, the need to create libraries to collect, organize and disseminate these types of resources is felt. With the growth of electronic resources, resource management has gained special importance and is one of the important areas and issues in the discussion of digital libraries. In this study, the aim is to examine the issues and challenges facing the management of digital libraries and provide solutions to solve the challenges and issues facing digital libraries and digital library management. Research method: The current research is applied in terms of purpose and survey research in terms of method. The current research has been conducted by field method and using library techniques, and the researchers have presented digital library management approaches by reviewing the published texts on digital libraries and digital library management issues. Findings: The results of the research showed that the most important components of digital library management include human resources, management of shared resources, author's right to update resources, cataloging and maintaining the technical structure. Also, the surveys showed that the most important challenge facing digital libraries is the issue of intellectual property and compliance with copyright laws. Conclusion: The results of the research showed that in digital libraries, as in traditional libraries, measures must be taken in the field of collecting, organizing, storing and disseminating information, and it is not possible to carry out the above-mentioned activities without a competent manager. Digital library management leads to the creation of coordination between different parts of the digital library and helps the library to achieve the desired goals. The digital library is facing many issues and challenges, including financial and budget issues, issues related to expert human resources, issues related to digital equipment and internet infrastructure, issues related to author's right and copyright, issues related to the lack of devices. Digitization and security of important information resources and documents and finally issues related to the protection and maintenance of digital resources are faced, which cannot be solved except with the presence of a capable manager and strong human resources of the library.

Summary This paper investigates the robust downlink beamforming designs based on max–min fairness and base station (BS) power consumption constraint for device‐to‐device (D2D) communications underlaying cellular network, under the assumption of imperfect channel state information (CSI) at the BS. Our objective is to maximize the minimum signal‐to‐interference‐plus‐noise ratio (SINR) or non‐outage probability of users while guaranteeing that the consumed power at the BS is less than a threshold. In particular, three max–min fairness scenarios are considered. In the first scenario, the worst‐case SINR of cellular users (CUs) is maximized where the D2D SINR is guaranteed to be above a specified predetermined threshold. In the second scenario, we extend the first scenario and maximized D2D SINR while maximizing CUs' SINR. In these two scenarios, it is assumed that the errors are upper bounded in their Frobenius norms. In the third scenario, the minimum non‐outage probability of users is maximized, while a probabilistic model is considered for the uncertainty of channel covariance matrices. Although such optimization problems are not convex, the semidefinite relaxation (SDR) approach is used to obtain the optimal beamforming matrix, which always complies the rank‐one constraint. Simulation results show that significant improvement in terms of minimum SINR of CUs, the minimum non‐outage probability of CUs, and the probability of feasibility and the fairness index can be achieved with our proposed algorithms in comparison with other beamforming schemes.

The possibility of producing a measurable long-lived dark $Z$ boson, that is assumed to mix kinetically with the hypercharge gauge boson in Higgs decays and to be produced also in Higgs decays through Higgs-to-dark-Higgs mixing, at the Large Hadron Collider (LHC) is investigated. Displaced dimuons in the final state are considered where each of the $Z$ and the dark $Z$ bosons decays directly to a dimuon. The total cross sections for the decay modes of interest as well as the decay widths and decay lengths are calculated to next-to-leading order (NLO) by using Monte Carlo (MC) simulation in the framework of {\textsc{MadGraph5}}\_aMC@NLO and compared to the available analytical calculations to leading order (LO). The sensitivity of the LHC in Runs 2 and 3 to such searches is discussed.