Modares Journal of Electrical Engineering, Jul 14, 2005
This paper introduces a technique for controlling a class of uncertain chaotic systems using an a... more This paper introduces a technique for controlling a class of uncertain chaotic systems using an adaptive fuzzy Proportional-Integrator-Derivative (PID) controller with H∞ tracking performance. The purpose of this work is to achieve optimal tracking performance of the controller using Backtracking Search Algorithm (BSA). BSA, which is a novel heuristic algorithm, has an easy structure with single control parameter. In BSA, three basic genetic operators (selection, mutation and crossover) are utilized to generate trial individuals. To this reason, the control problem in hand is considered as an optimization problem by defining an appropriate objective function. Stability analysis of the control scheme is provided based on Lyapunov theory and modified Riccati-like equation, where the robustness of the closed-loop system is guaranteed by H∞ tracking performance for any predefined level. To evaluate the performance of the proposed control method, it is employed for tracking control of Duffing uncertain chaotic system. Simulation results show the capability of the proposed controller.
Engineering Applications of Artificial Intelligence, Oct 12, 2010
This article appeared in a journal published by Elsevier. The attached copy is furnished to the a... more This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright
In this paper, Teaching-Learning-Based Optimization (TLBO) algorithm is employed for controlling ... more In this paper, Teaching-Learning-Based Optimization (TLBO) algorithm is employed for controlling the speed of induction motors using fuzzy sliding mode controller. The proposed control scheme formulates the design of the controller as an optimization problem. First, a sliding mode speed controller with an integral switching surface is designed, in which the acceleration information for speed control is not required. In this case, the upper bound of the lumped uncertainties including the parameter uncertainties and the load disturbance must be available. The importance of this parameter on the system performance is illustrated. Then, the fuzzy sliding mode speed controller is designed to estimate the upper bound of the lumped uncertainties. Finally, TLBO algorithm is adopted to determine the optimal upper bound of the uncertainty. Simulation results are given to demonstrate the superiority of the proposed controller in comparison with the proportionalintegrator, traditional sliding mode controller, fuzzy sliding mode controller and adaptive fuzzy sliding mode controller.
This paper introduces a novel control methodology based on fuzzy controller for a glucose-insulin... more This paper introduces a novel control methodology based on fuzzy controller for a glucose-insulin regulatory system of type I diabetes patient. First, in order to incorporate knowledge about patient treatment, a fuzzy logic controller is employed for regulating the gains of the basis Proportional-Integral (PI) as a self-tuning controller. Then, to overcome the key drawback of fuzzy logic controller, i.e., the lack of systematic methods to define fuzzy rules and fuzzy membership functions, fuzzy PI controller are optimized by Particle Swarm Optimization with Linearly Decreasing Weight (LDW-PSO) algorithm, which is a novel evolutionary computation technique. Simulation results show the effectiveness of the proposed optimal fuzzy PI controller in terms of accuracy and time margin.
Turkish Journal of Electrical Engineering and Computer Sciences, 2013
Diabetes is a chronic disease in which there are high levels of sugar in the blood. Insulin is a ... more Diabetes is a chronic disease in which there are high levels of sugar in the blood. Insulin is a hormone that regulates the blood glucose level in the body. Diabetes mellitus can be caused by too little insulin, a resistance to insulin, or both. Although research activities on controlling blood glucose have been attempted to lower the blood glucose level in the quickest possible time, there are some shortages in the amount of the insulin injection. In this paper, a complete model of the glucose-insulin regulation system, which is a nonlinear delay differential model, is used. The purpose of this paper is to follow the glucose profiles of a healthy person with minimum infused insulin. To achieve these purposes, an intelligent fuzzy controller based on a Mamdani-type structure, namely the swarm optimization tuned Mamdani fuzzy controller, is proposed for type 1 diabetic patients. The proposed fuzzy controller is optimized by a novel heuristic algorithm, namely linearly decreasing weight particle swarm optimization. To verify the robust performance of the proposed controller, a group of 4 tests is applied. Insensitivity to multiple meal disturbances, high accuracy, and superior robustness to model the parameter uncertainties are the key aspects of the proposed method. The simulation results illustrate the superiority of the proposed controller.
In this research work, we deal with the stabilization of uncertain fractional-order neutral syste... more In this research work, we deal with the stabilization of uncertain fractional-order neutral systems with delayed input. To tackle this problem, the guaranteed cost control method is considered. The purpose is to design a proportional–differential output feedback controller to obtain a satisfactory performance. The stability of the overall system is described in terms of matrix inequalities, and the corresponding analysis is performed in the perspective of Lyapunov’s theory. Two application examples verify the analytic findings.
Journal of Control Engineering and Applied Informatics, Dec 24, 2020
This article seeks to investigate a robust active fault-tolerant control strategy for a wind turb... more This article seeks to investigate a robust active fault-tolerant control strategy for a wind turbine system in the presence of actuator and sensor fault. The state-space representation of the system was formulated by the Takagi-Sugeno fuzzy model and then, a disturbance rejection technique is used to eliminate the wind perturbation. To guarantee the robust behavior of the system, the control signal is reconfigured through adding a robust term. By using the Lyapunov method, some criteria, which are expressed in the form of linear matrix inequalities (LMIs), are provided for asymptotic stability of the estimated error. Finally, the main results were confirmed by numerical simulations of a 1 MW wind turbine.
The penetration level of the photovoltaic (PV) systems is growing in the distribution networks th... more The penetration level of the photovoltaic (PV) systems is growing in the distribution networks throughout the world. On the other hand, the voltage drop across the feeder and the voltage imbalance are important issues in radial distribution networks. One of the most effective methods to deal with these problems is reactive power injection by PV-based multiple distributed static compensators (D-Statcom). Hence, a method based on the integral to droop line algorithm, which can regulate the reactive current injection for the voltage control by optimizing the droop coefficient and integral gain, has been proposed in this paper. Therefore, genetic algorithm (GA) is used to minimize the voltage deviation (VD) and voltage unbalanced factor (VUF). The proposed method has been simulated and evaluated on the typical low voltage (LV) 3-phase distribution network. The results indicate that the voltage profile along the feeder has been improved from a poor range to the acceptable range of 0.95 t...
The topic of Doppler and Bearing Tracking (DBT) problem is to achieve a target trajectory using t... more The topic of Doppler and Bearing Tracking (DBT) problem is to achieve a target trajectory using the Doppler and Bearing measurements. The difficulty of DBT problem comes from the nonlinearity terms exposed in the measurement equations. Several techniques were studied to deal with this topic, such as the unscented Kalman filter. Nevertheless, the performance of the filter depends directly on the prior knowledge, involving the accurate model, sufficient information of the noise distribution and the suitable initialization. To address these problems, in this paper, a new adaptive factor together with a fuzzy logic system is proposed for online adjusting the process and the measurement noise covariance matrices simultaneously. In the core of the proposed algorithm, the fault detection procedure is also adopted to reduce the computational time. The theoretical developments are investigated by simulations, which indicate the effectiveness of the proposed filter in DBT problem.
International Journal of Nonlinear Analysis and Applications, 2020
In all developed countries, energy systems are being adapted to employ sustainable energies as su... more In all developed countries, energy systems are being adapted to employ sustainable energies as such these countries are developing some programs to reduce the usage of fossil energy as much as possible in order to avoid environmental pollution and make the world a better place to live. The use of electrical vehicle (EV) is one of the appropriate options in this regard. In this paper, the power of charging stations, load uncertainty, and the uncertainty of electricity price in power systems were modeled using the behaviors of EV owners and a two-point estimate method, respectively. Then the contribution coefficient of charging stations and wind generation units as a distribution system were optimized using the NSBSA algorithm. Simulation was performed in MATLAB software, and IEEE 9-bus test system validated the efficiency of this algorithm.
Abstract This paper presents a comprehensive study of the Particle Swarm Optimization (PSO) algor... more Abstract This paper presents a comprehensive study of the Particle Swarm Optimization (PSO) algorithm, called complex-order PSO (CPSO). In the core of new set of algorithms, we employ the complex-order derivative and the conjugate order differential concepts in the position and velocity adaption mechanisms. To determine the influence of the control parameters on the quality of the results, a sensitivity analysis is conducted. A number of value- and rank-based tests assesses the algorithms’ performance. For a suite of benchmark functions, the standard deviation and the mean best of the results are reported. Additionally, the Friedman test specifies the average ranking from the obtained results. The effect of the complex-order operation and the population size are analyzed using the Taguchi test. An application example illustrates the performance of the CPSO.
Abstract A triaxial microelectromechanical system (MEMS) accelerometer is a low-cost sensor for m... more Abstract A triaxial microelectromechanical system (MEMS) accelerometer is a low-cost sensor for measuring the acceleration. However, the measured values by the sensor are generally noisy and inaccurate. Therefore, calibration algorithms need to be used for the calibration of MEMS accelerometers, such as the field calibration. In the case of an accelerometer, using the magnitude of the gravity vector as a stable reference leads to a nonlinear optimization problem. In this paper, a modified version of the Cuckoo Optimization Algorithm (COA), namely Unequal Limit COA (ULCOA), is introduced to achieve the optimal calibration parameters. Then, its performance is evaluated via a set of nonlinear benchmark functions indicating outperformance of the ULCOA in comparison with the particle swarm optimization and the genetic algorithms in terms of accuracy and robustness. Afterward, the ULCOA-based field calibration for the triaxial MEMS accelerometer is discussed. Finally, experimental results are provided and compared with other calibration methods.
This paper studies the synchronization of a class of uncertain fractional order (FO) chaotic syst... more This paper studies the synchronization of a class of uncertain fractional order (FO) chaotic systems that is applicable in secure communication. A novel hybrid FO controller, based on sliding mode and state feedback techniques combined with fuzzy logic, is developed. The algorithm, derived via the fractional Lyapunov theory, guarantees the stability of the overall system and the convergence of the synchronization errors toward a small residual set. Simulations demonstrate the capability of the proposed control algorithm in secure communications, not only in terms of speed of response, but also by reducing the chattering phenomenon.
This paper deals with the uniform stability of the Fractional Order Leaky Integrator Echo State N... more This paper deals with the uniform stability of the Fractional Order Leaky Integrator Echo State Neural Network (FOESN) with multiple delays. The delays occur in the transmission, the readout and the leakage of the network and have constant values. Sufficient conditions for uniform intrinsical stability of such networks in the presence of delays are provided. The intrinsical stability guarantees the FOESN is stable independently of the delays. In addition, the existence and uniqueness of the equilibrium point using the contraction mapping theorem are derived. Simulation results illustrate the effectiveness of the proposed method.
This paper is concerned with the problem of finite-time H∞ stability analysis of uncertain discre... more This paper is concerned with the problem of finite-time H∞ stability analysis of uncertain discrete-time Networked Control Systems (NCSs) with varying communication delays in a random fashion. Both measurement and actuation delays are modeled by two independent Bernoulli distributed white sequences. A dynamic output feedback controller is designed to realize finite time control for this class of NCSs with prescribed H∞ performance level. An iterative algorithm is developed to compute the controller's parameters by means of the Cone Complementarity Linearization Method (CCLM). The validity and feasibility of the proposed stability criterion are confirmed via numerical simulation examples.
An important problem in engineering is the unknown parameters estimation in nonlinear systems. In... more An important problem in engineering is the unknown parameters estimation in nonlinear systems. In this paper, a novel adaptive particle swarm optimization (APSO) method is proposed to solve this problem. This work considers two new aspects, namely an adaptive mutation mechanism and a dynamic inertia weight into the conventional particle swarm optimization (PSO) method. These mechanisms are employed to enhance global search ability and to increase accuracy. First, three well-known benchmark functions namely Griewank, Rosenbrock and Rastrigrin are utilized to test the ability of a search algorithm for identifying the global optimum. The performance of the proposed APSO is compared with advanced algorithms such as a nonlinearly decreasing weight PSO (NDWPSO) and a real-coded genetic algorithm (GA), in terms of parameter accuracy and convergence speed. It is confirmed that the proposed APSO is more successful than other aforementioned algorithms. Finally, the feasibility of this algorithm is demonstrated through estimating the parameters of two kinds of highly nonlinear systems as the case studies.
Modares Journal of Electrical Engineering, Jul 14, 2005
This paper introduces a technique for controlling a class of uncertain chaotic systems using an a... more This paper introduces a technique for controlling a class of uncertain chaotic systems using an adaptive fuzzy Proportional-Integrator-Derivative (PID) controller with H∞ tracking performance. The purpose of this work is to achieve optimal tracking performance of the controller using Backtracking Search Algorithm (BSA). BSA, which is a novel heuristic algorithm, has an easy structure with single control parameter. In BSA, three basic genetic operators (selection, mutation and crossover) are utilized to generate trial individuals. To this reason, the control problem in hand is considered as an optimization problem by defining an appropriate objective function. Stability analysis of the control scheme is provided based on Lyapunov theory and modified Riccati-like equation, where the robustness of the closed-loop system is guaranteed by H∞ tracking performance for any predefined level. To evaluate the performance of the proposed control method, it is employed for tracking control of Duffing uncertain chaotic system. Simulation results show the capability of the proposed controller.
Engineering Applications of Artificial Intelligence, Oct 12, 2010
This article appeared in a journal published by Elsevier. The attached copy is furnished to the a... more This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright
In this paper, Teaching-Learning-Based Optimization (TLBO) algorithm is employed for controlling ... more In this paper, Teaching-Learning-Based Optimization (TLBO) algorithm is employed for controlling the speed of induction motors using fuzzy sliding mode controller. The proposed control scheme formulates the design of the controller as an optimization problem. First, a sliding mode speed controller with an integral switching surface is designed, in which the acceleration information for speed control is not required. In this case, the upper bound of the lumped uncertainties including the parameter uncertainties and the load disturbance must be available. The importance of this parameter on the system performance is illustrated. Then, the fuzzy sliding mode speed controller is designed to estimate the upper bound of the lumped uncertainties. Finally, TLBO algorithm is adopted to determine the optimal upper bound of the uncertainty. Simulation results are given to demonstrate the superiority of the proposed controller in comparison with the proportionalintegrator, traditional sliding mode controller, fuzzy sliding mode controller and adaptive fuzzy sliding mode controller.
This paper introduces a novel control methodology based on fuzzy controller for a glucose-insulin... more This paper introduces a novel control methodology based on fuzzy controller for a glucose-insulin regulatory system of type I diabetes patient. First, in order to incorporate knowledge about patient treatment, a fuzzy logic controller is employed for regulating the gains of the basis Proportional-Integral (PI) as a self-tuning controller. Then, to overcome the key drawback of fuzzy logic controller, i.e., the lack of systematic methods to define fuzzy rules and fuzzy membership functions, fuzzy PI controller are optimized by Particle Swarm Optimization with Linearly Decreasing Weight (LDW-PSO) algorithm, which is a novel evolutionary computation technique. Simulation results show the effectiveness of the proposed optimal fuzzy PI controller in terms of accuracy and time margin.
Turkish Journal of Electrical Engineering and Computer Sciences, 2013
Diabetes is a chronic disease in which there are high levels of sugar in the blood. Insulin is a ... more Diabetes is a chronic disease in which there are high levels of sugar in the blood. Insulin is a hormone that regulates the blood glucose level in the body. Diabetes mellitus can be caused by too little insulin, a resistance to insulin, or both. Although research activities on controlling blood glucose have been attempted to lower the blood glucose level in the quickest possible time, there are some shortages in the amount of the insulin injection. In this paper, a complete model of the glucose-insulin regulation system, which is a nonlinear delay differential model, is used. The purpose of this paper is to follow the glucose profiles of a healthy person with minimum infused insulin. To achieve these purposes, an intelligent fuzzy controller based on a Mamdani-type structure, namely the swarm optimization tuned Mamdani fuzzy controller, is proposed for type 1 diabetic patients. The proposed fuzzy controller is optimized by a novel heuristic algorithm, namely linearly decreasing weight particle swarm optimization. To verify the robust performance of the proposed controller, a group of 4 tests is applied. Insensitivity to multiple meal disturbances, high accuracy, and superior robustness to model the parameter uncertainties are the key aspects of the proposed method. The simulation results illustrate the superiority of the proposed controller.
In this research work, we deal with the stabilization of uncertain fractional-order neutral syste... more In this research work, we deal with the stabilization of uncertain fractional-order neutral systems with delayed input. To tackle this problem, the guaranteed cost control method is considered. The purpose is to design a proportional–differential output feedback controller to obtain a satisfactory performance. The stability of the overall system is described in terms of matrix inequalities, and the corresponding analysis is performed in the perspective of Lyapunov’s theory. Two application examples verify the analytic findings.
Journal of Control Engineering and Applied Informatics, Dec 24, 2020
This article seeks to investigate a robust active fault-tolerant control strategy for a wind turb... more This article seeks to investigate a robust active fault-tolerant control strategy for a wind turbine system in the presence of actuator and sensor fault. The state-space representation of the system was formulated by the Takagi-Sugeno fuzzy model and then, a disturbance rejection technique is used to eliminate the wind perturbation. To guarantee the robust behavior of the system, the control signal is reconfigured through adding a robust term. By using the Lyapunov method, some criteria, which are expressed in the form of linear matrix inequalities (LMIs), are provided for asymptotic stability of the estimated error. Finally, the main results were confirmed by numerical simulations of a 1 MW wind turbine.
The penetration level of the photovoltaic (PV) systems is growing in the distribution networks th... more The penetration level of the photovoltaic (PV) systems is growing in the distribution networks throughout the world. On the other hand, the voltage drop across the feeder and the voltage imbalance are important issues in radial distribution networks. One of the most effective methods to deal with these problems is reactive power injection by PV-based multiple distributed static compensators (D-Statcom). Hence, a method based on the integral to droop line algorithm, which can regulate the reactive current injection for the voltage control by optimizing the droop coefficient and integral gain, has been proposed in this paper. Therefore, genetic algorithm (GA) is used to minimize the voltage deviation (VD) and voltage unbalanced factor (VUF). The proposed method has been simulated and evaluated on the typical low voltage (LV) 3-phase distribution network. The results indicate that the voltage profile along the feeder has been improved from a poor range to the acceptable range of 0.95 t...
The topic of Doppler and Bearing Tracking (DBT) problem is to achieve a target trajectory using t... more The topic of Doppler and Bearing Tracking (DBT) problem is to achieve a target trajectory using the Doppler and Bearing measurements. The difficulty of DBT problem comes from the nonlinearity terms exposed in the measurement equations. Several techniques were studied to deal with this topic, such as the unscented Kalman filter. Nevertheless, the performance of the filter depends directly on the prior knowledge, involving the accurate model, sufficient information of the noise distribution and the suitable initialization. To address these problems, in this paper, a new adaptive factor together with a fuzzy logic system is proposed for online adjusting the process and the measurement noise covariance matrices simultaneously. In the core of the proposed algorithm, the fault detection procedure is also adopted to reduce the computational time. The theoretical developments are investigated by simulations, which indicate the effectiveness of the proposed filter in DBT problem.
International Journal of Nonlinear Analysis and Applications, 2020
In all developed countries, energy systems are being adapted to employ sustainable energies as su... more In all developed countries, energy systems are being adapted to employ sustainable energies as such these countries are developing some programs to reduce the usage of fossil energy as much as possible in order to avoid environmental pollution and make the world a better place to live. The use of electrical vehicle (EV) is one of the appropriate options in this regard. In this paper, the power of charging stations, load uncertainty, and the uncertainty of electricity price in power systems were modeled using the behaviors of EV owners and a two-point estimate method, respectively. Then the contribution coefficient of charging stations and wind generation units as a distribution system were optimized using the NSBSA algorithm. Simulation was performed in MATLAB software, and IEEE 9-bus test system validated the efficiency of this algorithm.
Abstract This paper presents a comprehensive study of the Particle Swarm Optimization (PSO) algor... more Abstract This paper presents a comprehensive study of the Particle Swarm Optimization (PSO) algorithm, called complex-order PSO (CPSO). In the core of new set of algorithms, we employ the complex-order derivative and the conjugate order differential concepts in the position and velocity adaption mechanisms. To determine the influence of the control parameters on the quality of the results, a sensitivity analysis is conducted. A number of value- and rank-based tests assesses the algorithms’ performance. For a suite of benchmark functions, the standard deviation and the mean best of the results are reported. Additionally, the Friedman test specifies the average ranking from the obtained results. The effect of the complex-order operation and the population size are analyzed using the Taguchi test. An application example illustrates the performance of the CPSO.
Abstract A triaxial microelectromechanical system (MEMS) accelerometer is a low-cost sensor for m... more Abstract A triaxial microelectromechanical system (MEMS) accelerometer is a low-cost sensor for measuring the acceleration. However, the measured values by the sensor are generally noisy and inaccurate. Therefore, calibration algorithms need to be used for the calibration of MEMS accelerometers, such as the field calibration. In the case of an accelerometer, using the magnitude of the gravity vector as a stable reference leads to a nonlinear optimization problem. In this paper, a modified version of the Cuckoo Optimization Algorithm (COA), namely Unequal Limit COA (ULCOA), is introduced to achieve the optimal calibration parameters. Then, its performance is evaluated via a set of nonlinear benchmark functions indicating outperformance of the ULCOA in comparison with the particle swarm optimization and the genetic algorithms in terms of accuracy and robustness. Afterward, the ULCOA-based field calibration for the triaxial MEMS accelerometer is discussed. Finally, experimental results are provided and compared with other calibration methods.
This paper studies the synchronization of a class of uncertain fractional order (FO) chaotic syst... more This paper studies the synchronization of a class of uncertain fractional order (FO) chaotic systems that is applicable in secure communication. A novel hybrid FO controller, based on sliding mode and state feedback techniques combined with fuzzy logic, is developed. The algorithm, derived via the fractional Lyapunov theory, guarantees the stability of the overall system and the convergence of the synchronization errors toward a small residual set. Simulations demonstrate the capability of the proposed control algorithm in secure communications, not only in terms of speed of response, but also by reducing the chattering phenomenon.
This paper deals with the uniform stability of the Fractional Order Leaky Integrator Echo State N... more This paper deals with the uniform stability of the Fractional Order Leaky Integrator Echo State Neural Network (FOESN) with multiple delays. The delays occur in the transmission, the readout and the leakage of the network and have constant values. Sufficient conditions for uniform intrinsical stability of such networks in the presence of delays are provided. The intrinsical stability guarantees the FOESN is stable independently of the delays. In addition, the existence and uniqueness of the equilibrium point using the contraction mapping theorem are derived. Simulation results illustrate the effectiveness of the proposed method.
This paper is concerned with the problem of finite-time H∞ stability analysis of uncertain discre... more This paper is concerned with the problem of finite-time H∞ stability analysis of uncertain discrete-time Networked Control Systems (NCSs) with varying communication delays in a random fashion. Both measurement and actuation delays are modeled by two independent Bernoulli distributed white sequences. A dynamic output feedback controller is designed to realize finite time control for this class of NCSs with prescribed H∞ performance level. An iterative algorithm is developed to compute the controller's parameters by means of the Cone Complementarity Linearization Method (CCLM). The validity and feasibility of the proposed stability criterion are confirmed via numerical simulation examples.
An important problem in engineering is the unknown parameters estimation in nonlinear systems. In... more An important problem in engineering is the unknown parameters estimation in nonlinear systems. In this paper, a novel adaptive particle swarm optimization (APSO) method is proposed to solve this problem. This work considers two new aspects, namely an adaptive mutation mechanism and a dynamic inertia weight into the conventional particle swarm optimization (PSO) method. These mechanisms are employed to enhance global search ability and to increase accuracy. First, three well-known benchmark functions namely Griewank, Rosenbrock and Rastrigrin are utilized to test the ability of a search algorithm for identifying the global optimum. The performance of the proposed APSO is compared with advanced algorithms such as a nonlinearly decreasing weight PSO (NDWPSO) and a real-coded genetic algorithm (GA), in terms of parameter accuracy and convergence speed. It is confirmed that the proposed APSO is more successful than other aforementioned algorithms. Finally, the feasibility of this algorithm is demonstrated through estimating the parameters of two kinds of highly nonlinear systems as the case studies.
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