2021 12th Power Electronics, Drive Systems, and Technologies Conference (PEDSTC), 2021
Nowadays, due to availability of powerful signal processors, the digital control approaches, such... more Nowadays, due to availability of powerful signal processors, the digital control approaches, such as deadbeat control, have received considerable attentions. The deadbeat controller offers critical advantages, such as constant switching frequency, fast dynamic response, and low settling time. Nevertheless, the parameter dependency of the deadbeat controller has always been questioned. In this regard, this paper proposes a forward-backward discretization method for a single-phase active power filter to be used for deadbeat controller design. This procedure offers high accuracy in modeling and at the same time simplicity in designing the deadbeat controller. The proposed discretization approach reduces the required two forward steps prediction down to only a step. The superiority of the developed controller is then confirmed through extensive simulations.
Abstract— This paper presents robust optimal control of an uncertain nonlinear switched system wi... more Abstract— This paper presents robust optimal control of an uncertain nonlinear switched system with forced subsystems. The uncertainties include external disturbance and parametric uncertainties. Switching signal and control input are designed to minimize a given cost function. Approximate dynamic programming (ADP) has been efficiently applied to certain switched systems as an optimal control strategy. Since approximate dynamic programming method is model based, there would seem to be some difficulties to apply approximate dynamic programming to uncertain switched system. To overcome these mentioned problems, this paper presents an appropriate model. In order to apply proposed control approach, robust time-delay controller is added with ADP control. At first uncertainties are compensated by robust timedelay controller. Then the switching signal and the control input are design by approximate dynamic programming that provides a feedback solution for unspecified initial conditions. Th...
In this paper, a novel scheme based on sliding mode control method for impedance control of a sin... more In this paper, a novel scheme based on sliding mode control method for impedance control of a single link flexible robot arm when it comes into contact with unknown environment, is presented. The proposed control strategy is robust against the changes of the environment parameters (such as stiffness and damping coefficient), the unknown Coulomb friction disturbances, payload and viscous friction variations. The proposed scheme is also valid for both constrained and unconstrained motions. In our new approach, the controller automatically switches from a free to a constrained motion mode therefore it does not need an algorithm to detect collision between the link and the environment. In this regard, impedance control is proposed with the inner loop position. This means that in the free motion, the applied force to the environment is zero and the reference trajectory for the inner loop position is the desired trajectory. In the constrained motion, the reference trajectory for the inner...
This paper proposes a new method for the identification of switched linear systems. The proposed ... more This paper proposes a new method for the identification of switched linear systems. The proposed method includes two main steps of mapping and clustering. At the first step, a mapping is developed from the space of input-output data into the parameter space. A lot of linear equation sets, composed of equal number of equations and unknowns, are solved in this part. At the next step, submodel parameters are derived by clustering the parameters obtained in previous step, into several groups. Since the clustering step is carried out in the parameter space, the proposed method makes no distinction between the identification of switched linear systems and piecewise linear systems and the identification of submodel parameters is done independently of the estimation of switching signal. Numerical examples show the effectiveness of the proposed method in the identification of switched linear systems.
This paper investigates stabilization for a class of nonlinear impulsive switched systems with no... more This paper investigates stabilization for a class of nonlinear impulsive switched systems with norm-bounded input constraint. Due to this constraint, it is only enough that the stabilization criteria and assumptions related to the nonlinearities be met on a subspace containing the origin. Certainly, these assumptions are such that they covers most of real-world systems. The purpose of this paper is to design a norm-bounded control that guarantees the exponential convergence of trajectories to a sufficient small ultimate bound in presence of uncertainties. Therefore, firstly, we present the stability criteria for a general model that ensures the convergence of all trajectories starting from a region of attraction to an ultimate bound. These conditions are in terms of a common Lyapunov function candidate and the minimum dwell-time, and it is enough to be valid on the region of attraction. Secondly, using the common quadratic Lyapunov function candidate and using the state-feedback app...
This paper presents a novel hybrid technique based on the modal series method and linear programm... more This paper presents a novel hybrid technique based on the modal series method and linear programming strategy for solving the optimal control problem of nonlinear fractional-order systems. The fractional derivative is defined in the sense of Riemann-Liouville with order less than one. The performance index includes the terminal cost in addition to the integral quadratic cost functional. Both the fixed and free final states cases have been taken into account. In this approach, first we extend the modal series method in order to convert the original nonlinear fractional-order two point boundary value problem (FTPBVP) derived from the Pontryagin’s maximum principle into a sequence of linear time-invariant FTPBVPs. This sequence is then transformed into a sequence of linear programming problems by defining a new variational problem in the calculus of D ow nl oa de d fr om jo c. kn tu .a c. ir at 1 :0 1 + 04 30 o n S un da y M ay 3 0t h 20 21 52 هتسد هنيهب لرتنک متسيس زا یا لادوم یرس زا ...
International Journal of Innovative Computing Information and Control, 2011
This paper presents a new approach to solve a class of nonlinear optimal control problems which h... more This paper presents a new approach to solve a class of nonlinear optimal control problems which have a quadratic performance index. In this approach, the nonlin- ear two-point boundary value problem (TPBVP), derived from the Pontryagin 's maximum principle, is transformed into a sequence of linear time-invariant TPBVP's. Solving the proposed linear TPBVP sequence in a recursive manner leads to the optimal control law and the optimal trajectory in the form of uniformly convergent series. Hence, to obtain the optimal solution, only the techniques of solving linear ordinary differential equations are employed. In order to use the proposed method in practice, a control design algorithm with low computational complexity and fast convergence rate is presented. Through the �nite iterations of algorithm, a suboptimal control law is obtained for the nonlinear opti- mal control problem. Finally, numerical examples are included to demonstrate efficiency, simplicity and high accuracy of...
This paper describes a control system which automatically parks a scaled automobile inside a rect... more This paper describes a control system which automatically parks a scaled automobile inside a rectangular reduced space given certain conditions and making decisions based in fuzzy logic. The control is developed by the processing of entry variable data from simulated sensors of a specific scenario, and the run of three models in cascade to achieve a decision-action method. Finally, this paper shows a description of the way this project was achieved, and concludes with the acceptable results that a fuzzy control can provide in a management of this kind of mechanism by the use of taking decision models.
In this paper, a new method is introduced to study the stabilization and design of stabilizing sw... more In this paper, a new method is introduced to study the stabilization and design of stabilizing switching law for switched homogeneous systems as a class of switched nonlinear systems. The considered switched system has a number of homogeneous subsystems with desired degree and similar dilation coefficients. In this method, there is not any limitation about system dimension, homogeneous degree and dilation coefficients. The proposed method is based on existence of homogeneous common Lyapunov function for subsystems and using that, the stabilizing switching law is specified. In this method, a combined system of subsystems is introduced and in a theorem it is shown that the stability of combined system results in the stability of switched system with defined switching law. Thus the Lyapunov function of combined system is introduced as common Lyapunov function for switched system.
In this paper we numerically investigate the chaotic behaviours of the fractional-order Lorenz sy... more In this paper we numerically investigate the chaotic behaviours of the fractional-order Lorenz system and its synchronization. For the first time, a fractional chaotic synchronization using an Unscented Kalman Filter (UKF) is presented. The chaotic synchronization is implemented by the UKF design in the presence of process noise and measurement noise. To illustrate the effectiveness of the synchronization with the UKF method, a numerical example based on the fractional-order Lorenz dynamical system is presented and the results are compared to the Extended Kalman Filter (EKF) method.
This paper investigates the stabilization problem of an autonomous Linear Time Invariant (LTI) sw... more This paper investigates the stabilization problem of an autonomous Linear Time Invariant (LTI) switched system with interval uncertainty and unstable subsystems. It is proved that the system would be stable by using a common Lyapanov function whose derivative is negative and bounded by a quadratic function within activation regions of each subsystem. First, a sufficient condition for the stability of an Linear Time Invariant switched system with interval uncertainty, based on the convex analysis and interval set theoretical approach, is presented and proved. Moreover, conservatism in the stability robustness bound is obtained. Then, a switching control law is designed to shift the Linear Time Invariant switched system among subsystems to ensure the decrease of the Lyapanov function within the state space. Finally, in order to decrease the switching frequency and to avoid chattering, the switching law is modified. Two examples are included to demonstrate the effectiveness of the theo...
In this paper, estimation of second order polynomial systems’ domain of attraction (DA) via ratio... more In this paper, estimation of second order polynomial systems’ domain of attraction (DA) via rational Lyapunov function is investigated. One of the methods for estimating DA is to find the greatest level set. In this study, in order to obtain the greatest level set, cost function based on increasing the region enclosed to the level set has been offered instead of using shape factor. Estimating DA has been converted into solving bilinear matrix inequality optimization problem. Capacity of this method compared to other methods in recent studies has been shown through some examples.
Lyapunov's theorem is the basic criteria to establish the stability properties of the nonline... more Lyapunov's theorem is the basic criteria to establish the stability properties of the nonlinear dynamical systems. In this method, it is a necessity to find the positive definite functions with negative definite or negative semi-definite derivative. These functions that named Lyapunov functions, form the core of this criterion. The existence of the Lyapunov functions for asymptotically stable equilibrium points is guaranteed by converse Lyapunov theorems. On the other hand, for the cases where the equilibrium point is stable in the sense of Lyapunov, converse Lyapunov theorems only ensure non-smooth Lyapunov functions. In this paper, it is proved that there exist some autonomous nonlinear systems with stable equilibrium points that despite stability don’t admit convex Lyapunov functions. In addition, it is also shown that there exist some nonlinear systems that despite the fact that they are stable at the origin, but do not admit smooth Lyapunov functions in the form of V(x) or ...
A higher-order sliding approach to control a bioreactor model is proposed by non-commensurate fra... more A higher-order sliding approach to control a bioreactor model is proposed by non-commensurate fractional equations. The model outputs by the help of a controller reached the desired values and track them. According to existing conditions and chattering reduction, a high-order sliding mode has been chosen to design the controller. The purpose of the paper is to choose proper sliding surfaces. Here, for a better conclusion, a comparison has been made between the high-order sliding mode and the standard sliding mode. High-order sliding mode controllers have been taken in accordance with the structure of integer order system. Thus, in order for the system to apply more precise calculations, it should somehow turn to integer order. The sliding surfaces have been selected so appropriately that we can benefit from the structure of integer order controllers for fractional order system. The sliding surface in both controllers has also been the same so as to provide conditions for comparison....
Introduction: In this paper, a novel complexity measure is proposed to detect dynamical changes i... more Introduction: In this paper, a novel complexity measure is proposed to detect dynamical changes in nonlinear systems using ordinal pattern analysis of time series data taken from the system. Epilepsy is considered as a dynamical change in nonlinear and complex brain system. The ability of the proposed measure for characterizing the normal and epileptic EEG signals when the signal is short or is contaminated with noise is investigated and compared with some traditional chaos-based measures. Materials and Methods: In the proposed method, the phase space of the time series is reconstructed and then partitioned using ordinal patterns. The partitions can be labeled using a set of symbols. Therefore, the state trajectory is converted to a symbol sequence. A finite state machine is then constructed to model the sequence. A new complexity measure is proposed to detect dynamical changes using the state transition matrix of the state machine. The proposed complexity measure was applied to det...
2021 12th Power Electronics, Drive Systems, and Technologies Conference (PEDSTC), 2021
Nowadays, due to availability of powerful signal processors, the digital control approaches, such... more Nowadays, due to availability of powerful signal processors, the digital control approaches, such as deadbeat control, have received considerable attentions. The deadbeat controller offers critical advantages, such as constant switching frequency, fast dynamic response, and low settling time. Nevertheless, the parameter dependency of the deadbeat controller has always been questioned. In this regard, this paper proposes a forward-backward discretization method for a single-phase active power filter to be used for deadbeat controller design. This procedure offers high accuracy in modeling and at the same time simplicity in designing the deadbeat controller. The proposed discretization approach reduces the required two forward steps prediction down to only a step. The superiority of the developed controller is then confirmed through extensive simulations.
Abstract— This paper presents robust optimal control of an uncertain nonlinear switched system wi... more Abstract— This paper presents robust optimal control of an uncertain nonlinear switched system with forced subsystems. The uncertainties include external disturbance and parametric uncertainties. Switching signal and control input are designed to minimize a given cost function. Approximate dynamic programming (ADP) has been efficiently applied to certain switched systems as an optimal control strategy. Since approximate dynamic programming method is model based, there would seem to be some difficulties to apply approximate dynamic programming to uncertain switched system. To overcome these mentioned problems, this paper presents an appropriate model. In order to apply proposed control approach, robust time-delay controller is added with ADP control. At first uncertainties are compensated by robust timedelay controller. Then the switching signal and the control input are design by approximate dynamic programming that provides a feedback solution for unspecified initial conditions. Th...
In this paper, a novel scheme based on sliding mode control method for impedance control of a sin... more In this paper, a novel scheme based on sliding mode control method for impedance control of a single link flexible robot arm when it comes into contact with unknown environment, is presented. The proposed control strategy is robust against the changes of the environment parameters (such as stiffness and damping coefficient), the unknown Coulomb friction disturbances, payload and viscous friction variations. The proposed scheme is also valid for both constrained and unconstrained motions. In our new approach, the controller automatically switches from a free to a constrained motion mode therefore it does not need an algorithm to detect collision between the link and the environment. In this regard, impedance control is proposed with the inner loop position. This means that in the free motion, the applied force to the environment is zero and the reference trajectory for the inner loop position is the desired trajectory. In the constrained motion, the reference trajectory for the inner...
This paper proposes a new method for the identification of switched linear systems. The proposed ... more This paper proposes a new method for the identification of switched linear systems. The proposed method includes two main steps of mapping and clustering. At the first step, a mapping is developed from the space of input-output data into the parameter space. A lot of linear equation sets, composed of equal number of equations and unknowns, are solved in this part. At the next step, submodel parameters are derived by clustering the parameters obtained in previous step, into several groups. Since the clustering step is carried out in the parameter space, the proposed method makes no distinction between the identification of switched linear systems and piecewise linear systems and the identification of submodel parameters is done independently of the estimation of switching signal. Numerical examples show the effectiveness of the proposed method in the identification of switched linear systems.
This paper investigates stabilization for a class of nonlinear impulsive switched systems with no... more This paper investigates stabilization for a class of nonlinear impulsive switched systems with norm-bounded input constraint. Due to this constraint, it is only enough that the stabilization criteria and assumptions related to the nonlinearities be met on a subspace containing the origin. Certainly, these assumptions are such that they covers most of real-world systems. The purpose of this paper is to design a norm-bounded control that guarantees the exponential convergence of trajectories to a sufficient small ultimate bound in presence of uncertainties. Therefore, firstly, we present the stability criteria for a general model that ensures the convergence of all trajectories starting from a region of attraction to an ultimate bound. These conditions are in terms of a common Lyapunov function candidate and the minimum dwell-time, and it is enough to be valid on the region of attraction. Secondly, using the common quadratic Lyapunov function candidate and using the state-feedback app...
This paper presents a novel hybrid technique based on the modal series method and linear programm... more This paper presents a novel hybrid technique based on the modal series method and linear programming strategy for solving the optimal control problem of nonlinear fractional-order systems. The fractional derivative is defined in the sense of Riemann-Liouville with order less than one. The performance index includes the terminal cost in addition to the integral quadratic cost functional. Both the fixed and free final states cases have been taken into account. In this approach, first we extend the modal series method in order to convert the original nonlinear fractional-order two point boundary value problem (FTPBVP) derived from the Pontryagin’s maximum principle into a sequence of linear time-invariant FTPBVPs. This sequence is then transformed into a sequence of linear programming problems by defining a new variational problem in the calculus of D ow nl oa de d fr om jo c. kn tu .a c. ir at 1 :0 1 + 04 30 o n S un da y M ay 3 0t h 20 21 52 هتسد هنيهب لرتنک متسيس زا یا لادوم یرس زا ...
International Journal of Innovative Computing Information and Control, 2011
This paper presents a new approach to solve a class of nonlinear optimal control problems which h... more This paper presents a new approach to solve a class of nonlinear optimal control problems which have a quadratic performance index. In this approach, the nonlin- ear two-point boundary value problem (TPBVP), derived from the Pontryagin 's maximum principle, is transformed into a sequence of linear time-invariant TPBVP's. Solving the proposed linear TPBVP sequence in a recursive manner leads to the optimal control law and the optimal trajectory in the form of uniformly convergent series. Hence, to obtain the optimal solution, only the techniques of solving linear ordinary differential equations are employed. In order to use the proposed method in practice, a control design algorithm with low computational complexity and fast convergence rate is presented. Through the �nite iterations of algorithm, a suboptimal control law is obtained for the nonlinear opti- mal control problem. Finally, numerical examples are included to demonstrate efficiency, simplicity and high accuracy of...
This paper describes a control system which automatically parks a scaled automobile inside a rect... more This paper describes a control system which automatically parks a scaled automobile inside a rectangular reduced space given certain conditions and making decisions based in fuzzy logic. The control is developed by the processing of entry variable data from simulated sensors of a specific scenario, and the run of three models in cascade to achieve a decision-action method. Finally, this paper shows a description of the way this project was achieved, and concludes with the acceptable results that a fuzzy control can provide in a management of this kind of mechanism by the use of taking decision models.
In this paper, a new method is introduced to study the stabilization and design of stabilizing sw... more In this paper, a new method is introduced to study the stabilization and design of stabilizing switching law for switched homogeneous systems as a class of switched nonlinear systems. The considered switched system has a number of homogeneous subsystems with desired degree and similar dilation coefficients. In this method, there is not any limitation about system dimension, homogeneous degree and dilation coefficients. The proposed method is based on existence of homogeneous common Lyapunov function for subsystems and using that, the stabilizing switching law is specified. In this method, a combined system of subsystems is introduced and in a theorem it is shown that the stability of combined system results in the stability of switched system with defined switching law. Thus the Lyapunov function of combined system is introduced as common Lyapunov function for switched system.
In this paper we numerically investigate the chaotic behaviours of the fractional-order Lorenz sy... more In this paper we numerically investigate the chaotic behaviours of the fractional-order Lorenz system and its synchronization. For the first time, a fractional chaotic synchronization using an Unscented Kalman Filter (UKF) is presented. The chaotic synchronization is implemented by the UKF design in the presence of process noise and measurement noise. To illustrate the effectiveness of the synchronization with the UKF method, a numerical example based on the fractional-order Lorenz dynamical system is presented and the results are compared to the Extended Kalman Filter (EKF) method.
This paper investigates the stabilization problem of an autonomous Linear Time Invariant (LTI) sw... more This paper investigates the stabilization problem of an autonomous Linear Time Invariant (LTI) switched system with interval uncertainty and unstable subsystems. It is proved that the system would be stable by using a common Lyapanov function whose derivative is negative and bounded by a quadratic function within activation regions of each subsystem. First, a sufficient condition for the stability of an Linear Time Invariant switched system with interval uncertainty, based on the convex analysis and interval set theoretical approach, is presented and proved. Moreover, conservatism in the stability robustness bound is obtained. Then, a switching control law is designed to shift the Linear Time Invariant switched system among subsystems to ensure the decrease of the Lyapanov function within the state space. Finally, in order to decrease the switching frequency and to avoid chattering, the switching law is modified. Two examples are included to demonstrate the effectiveness of the theo...
In this paper, estimation of second order polynomial systems’ domain of attraction (DA) via ratio... more In this paper, estimation of second order polynomial systems’ domain of attraction (DA) via rational Lyapunov function is investigated. One of the methods for estimating DA is to find the greatest level set. In this study, in order to obtain the greatest level set, cost function based on increasing the region enclosed to the level set has been offered instead of using shape factor. Estimating DA has been converted into solving bilinear matrix inequality optimization problem. Capacity of this method compared to other methods in recent studies has been shown through some examples.
Lyapunov's theorem is the basic criteria to establish the stability properties of the nonline... more Lyapunov's theorem is the basic criteria to establish the stability properties of the nonlinear dynamical systems. In this method, it is a necessity to find the positive definite functions with negative definite or negative semi-definite derivative. These functions that named Lyapunov functions, form the core of this criterion. The existence of the Lyapunov functions for asymptotically stable equilibrium points is guaranteed by converse Lyapunov theorems. On the other hand, for the cases where the equilibrium point is stable in the sense of Lyapunov, converse Lyapunov theorems only ensure non-smooth Lyapunov functions. In this paper, it is proved that there exist some autonomous nonlinear systems with stable equilibrium points that despite stability don’t admit convex Lyapunov functions. In addition, it is also shown that there exist some nonlinear systems that despite the fact that they are stable at the origin, but do not admit smooth Lyapunov functions in the form of V(x) or ...
A higher-order sliding approach to control a bioreactor model is proposed by non-commensurate fra... more A higher-order sliding approach to control a bioreactor model is proposed by non-commensurate fractional equations. The model outputs by the help of a controller reached the desired values and track them. According to existing conditions and chattering reduction, a high-order sliding mode has been chosen to design the controller. The purpose of the paper is to choose proper sliding surfaces. Here, for a better conclusion, a comparison has been made between the high-order sliding mode and the standard sliding mode. High-order sliding mode controllers have been taken in accordance with the structure of integer order system. Thus, in order for the system to apply more precise calculations, it should somehow turn to integer order. The sliding surfaces have been selected so appropriately that we can benefit from the structure of integer order controllers for fractional order system. The sliding surface in both controllers has also been the same so as to provide conditions for comparison....
Introduction: In this paper, a novel complexity measure is proposed to detect dynamical changes i... more Introduction: In this paper, a novel complexity measure is proposed to detect dynamical changes in nonlinear systems using ordinal pattern analysis of time series data taken from the system. Epilepsy is considered as a dynamical change in nonlinear and complex brain system. The ability of the proposed measure for characterizing the normal and epileptic EEG signals when the signal is short or is contaminated with noise is investigated and compared with some traditional chaos-based measures. Materials and Methods: In the proposed method, the phase space of the time series is reconstructed and then partitioned using ordinal patterns. The partitions can be labeled using a set of symbols. Therefore, the state trajectory is converted to a symbol sequence. A finite state machine is then constructed to model the sequence. A new complexity measure is proposed to detect dynamical changes using the state transition matrix of the state machine. The proposed complexity measure was applied to det...
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