A new variable structure control algorithm based on sliding mode prediction for a class of discrete-time nonlinear systems is presented. By employing a special model to predict future sliding mode value, and combining...A new variable structure control algorithm based on sliding mode prediction for a class of discrete-time nonlinear systems is presented. By employing a special model to predict future sliding mode value, and combining feedback correction and receding horizon optimization methods which are extensively applied on predictive control strategy, a discrete-time variable structure control law is constructed. The closed-loop systems are proved to have robustness to uncertainties with unspecified boundaries. Numerical simulation and pendulum experiment results illustrate that the closed-loop systems possess desired performance, such as strong robustness, fast convergence and chattering elimination.展开更多
A new type criterion of globally uniformly ultimate boundedness for discrete-time nonlinear systems is introduced. In classical Lyapunov theory about globally uniformly ultimate boundedness, Lyapunov function is assum...A new type criterion of globally uniformly ultimate boundedness for discrete-time nonlinear systems is introduced. In classical Lyapunov theory about globally uniformly ultimate boundedness, Lyapunov function is assumed to be positive definite and its difference at the every latter moment and the former moment is negative definite. In this paper the condition of difference of Lyapunov function is relaxed. Under the relaxed condition, the result of this paper can be considered as the extension of the classical Lyapunov theory about uniformly ultimate boundedness.展开更多
In this paper, some computational tools are proposed to determine the largest invariant set, with respect to either a continuous-time or a discrete-time system, that is contained in an algebraic set. In particular, it...In this paper, some computational tools are proposed to determine the largest invariant set, with respect to either a continuous-time or a discrete-time system, that is contained in an algebraic set. In particular, it is shown that if the vector field governing the dynamics of the system is polynomial and the considered analytic set is a variety, then algorithms from algebraic geometry can be used to solve the considered problem. Examples of applications of the method(spanning from the characterization of the stability to the computation of the zero dynamics) are given all throughout the paper.展开更多
The robustly asymptotical stability problem for discrete-time nonlinear systems with time-delay was investigated. Positive definite matrix are constructed through Lyapunov functional. With the identity transform, prop...The robustly asymptotical stability problem for discrete-time nonlinear systems with time-delay was investigated. Positive definite matrix are constructed through Lyapunov functional. With the identity transform, property of matrix inverse and S-procedure, a new sufficient condition independent of the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is established. With Schur complement, another equivalent sufficient condition for robust stability of discrete-time nonlinear systems with time-delay is given. Finally, a sufficient condition dependent on the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is obtained. A unified approach is used to cast the robust stability problem into a convex optimization involving linear matrix inequalities.展开更多
An indirect adaptive fuzzy control scheme is developed for a class of nonlinear discrete-time systems. In this method, two fuzzy logic systems are used to approximate the unknown functions, and the parameters of membe...An indirect adaptive fuzzy control scheme is developed for a class of nonlinear discrete-time systems. In this method, two fuzzy logic systems are used to approximate the unknown functions, and the parameters of membership functions in fuzzy logic systems are adjusted according to adaptive laws for the purpose of controlling the plant to track a reference trajectory. It is proved that the scheme can not only guarantee the boundedness of the input and output of the closed-loop system, but also make the tracking error converge to a small neighborhood of the origin. Simulation results indicate the effectiveness of this scheme.展开更多
An uncertain nonlinear discrete-time system model with time-varying input delays for networked control systems (NCSs) is presented. The problem of exponential stability for the system is considered and some new criter...An uncertain nonlinear discrete-time system model with time-varying input delays for networked control systems (NCSs) is presented. The problem of exponential stability for the system is considered and some new criteria of exponential stability are obtained based on norm inequality methods. A numerical example is given todemonstrate that those criteria are useful to analyzing the stability of nonlinear NCSs.展开更多
Transient performance for output regulation problems of linear discrete-time systems with input saturation is addressed by using the composite nonlinear feedback（CNF） control technique. The regulator is designed to ...Transient performance for output regulation problems of linear discrete-time systems with input saturation is addressed by using the composite nonlinear feedback（CNF） control technique. The regulator is designed to be an additive combination of a linear regulator part and a nonlinear feedback part. The linear regulator part solves the regulation problem independently which produces a quick output response but large oscillations. The nonlinear feedback part with well-tuned parameters is introduced to improve the transient performance by smoothing the oscillatory convergence. It is shown that the introduction of the nonlinear feedback part does not change the solvability conditions of the linear discrete-time output regulation problem. The effectiveness of transient improvement is illustrated by a numeric example.展开更多
This paper proposes a discrete-time robust control technique for an uncertain nonlinear system. The uncertainty mainly affects the system dynamics due to mismatched parameter variation which is bounded by a predefined...This paper proposes a discrete-time robust control technique for an uncertain nonlinear system. The uncertainty mainly affects the system dynamics due to mismatched parameter variation which is bounded by a predefined known function. In order to compensate the effect of uncertainty, a robust control input is derived by formulating an equivalent optimal control problem for a virtual nominal system with a modified costfunctional. To derive the stabilizing control law for a mismatched system, this paper introduces another control input named as virtual input. This virtual input is not applied directly to stabilize the uncertain system, rather it is used to define a sufficient condition. To solve the nonlinear optimal control problem, a discretetime general Hamilton-Jacobi-Bellman(DT-GHJB) equation is considered and it is approximated numerically through a neural network(NN) implementation. The approximated solution of DTGHJB is used to compute the suboptimal control input for the virtual system. The suboptimal inputs for the virtual system ensure the asymptotic stability of the closed-loop uncertain system. A numerical example is illustrated with simulation results to prove the efficacy of the proposed control algorithm.展开更多
This paper presents a robust sliding mode controller for a class of unknown nonlinear discrete-time systems in the presence of fixed time delay. A neural-network approximation and the Lyapunov-Krasovskii functional th...This paper presents a robust sliding mode controller for a class of unknown nonlinear discrete-time systems in the presence of fixed time delay. A neural-network approximation and the Lyapunov-Krasovskii functional theory into the sliding-mode technique is used and a neural-network based sliding mode control scheme is proposed. Because of the novality of Chebyshev Neural Networks (CNNs), that it requires much less computation time as compare to multi layer neural network (MLNN), is preferred to approximate the unknown system functions. By means of linear matrix inequalities, a sufficient condition is derived to ensure the asymptotic stability such that the sliding mode dynamics is restricted to the defined sliding surface. The proposed sliding mode control technique guarantees the system state trajectory to the designed sliding surface. Finally, simulation results illustrate the main characteristics and performance of the proposed approach.展开更多
In this paper,we studied the approximate sampleddata observer design for a class of stochastic nonlinear systems.Euler-Maruyama approximation was investigated in this paper because it is the basis of other higher prec...In this paper,we studied the approximate sampleddata observer design for a class of stochastic nonlinear systems.Euler-Maruyama approximation was investigated in this paper because it is the basis of other higher precision numerical methods,and it preserves important structures of the nonlinear systems.Also,the form of Euler-Maruyama model is simple and easy to be calculated.The results provide a reference for sampled-data observer design method for such stochastic nonlinear systems,and may be useful to many practical control applications,such as tracking control in mechanical systems.And the effectiveness of the approach is demonstrated by a simulation example.展开更多
This paper discusses about the stabilization of unknown nonlinear discrete-time fixed state delay systems. The unknown system nonlinearity is approximated by Chebyshev neural network (CNN), and weight update law is pr...This paper discusses about the stabilization of unknown nonlinear discrete-time fixed state delay systems. The unknown system nonlinearity is approximated by Chebyshev neural network (CNN), and weight update law is presented for approximating the system nonlinearity. Using appropriate Lyapunov-Krasovskii functional the stability of the nonlinear system is ensured by the solution of linear matrix inequalities. Finally, a relevant example is given to illustrate the effectiveness of the proposed control scheme.展开更多
An event-triggered scheme is proposed to solve the problems of robust guaranteed cost control for a class of two-dimensional(2-D)discrete-time systems.Firstly,an eventtriggered scheme is proposed for 2-D discrete-time...An event-triggered scheme is proposed to solve the problems of robust guaranteed cost control for a class of two-dimensional(2-D)discrete-time systems.Firstly,an eventtriggered scheme is proposed for 2-D discrete-time systems with parameter uncertainties and sector nonlinearities.Then,according to the Lyapunov functional method,the sufficient conditions for the existence of event-triggered robust guaranteed cost controller for 2-D discrete-time systems with parameter uncertainties and sector nonlinearities are given.Furthermore,based on the sufficient conditions and the linear matrix inequality(LMI)technique,the problem of designing event-triggered robust guaranteed cost controller is transformed into a feasible solution problem of LMI.Finally,a numerical example is given to demonstrate that,under the proposed event-triggered robust guaranteed cost control,the closed-loop system is asymptotically stable and fewer communication resources are occupied.展开更多
In this paper, a computational approach is proposed for solving the discrete-time nonlinear optimal control problem, which is disturbed by a sequence of random noises. Because of the exact solution of such optimal con...In this paper, a computational approach is proposed for solving the discrete-time nonlinear optimal control problem, which is disturbed by a sequence of random noises. Because of the exact solution of such optimal control problem is impossible to be obtained, estimating the state dynamics is currently required. Here, it is assumed that the output can be measured from the real plant process. In our approach, the state mean propagation is applied in order to construct a linear model-based optimal control problem, where the model output is measureable. On this basis, an output error, which takes into account the differences between the real output and the model output, is defined. Then, this output error is minimized by applying the stochastic approximation approach. During the computation procedure, the stochastic gradient is established, so as the optimal solution of the model used can be updated iteratively. Once the convergence is achieved, the iterative solution approximates to the true optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, an example on a continuous stirred-tank reactor problem is studied, and the result obtained shows the applicability of the approach proposed. Hence, the efficiency of the approach proposed is highly recommended.展开更多
In this paper, a novel iterative Q-learning algorithm, called "policy iteration based deterministic Qlearning algorithm", is developed to solve the optimal control problems for discrete-time deterministic no...In this paper, a novel iterative Q-learning algorithm, called "policy iteration based deterministic Qlearning algorithm", is developed to solve the optimal control problems for discrete-time deterministic nonlinear systems. The idea is to use an iterative adaptive dynamic programming(ADP) technique to construct the iterative control law which optimizes the iterative Q function. When the optimal Q function is obtained, the optimal control law can be achieved by directly minimizing the optimal Q function, where the mathematical model of the system is not necessary. Convergence property is analyzed to show that the iterative Q function is monotonically non-increasing and converges to the solution of the optimality equation. It is also proven that any of the iterative control laws is a stable control law. Neural networks are employed to implement the policy iteration based deterministic Q-learning algorithm, by approximating the iterative Q function and the iterative control law, respectively. Finally, two simulation examples are presented to illustrate the performance of the developed algorithm.展开更多
The left-inverse system with minimal order and its algorithms of discrete-time nonlinear systems are studied in a linear algebraic framework. The general structure of left-inverse system is described and computed in s...The left-inverse system with minimal order and its algorithms of discrete-time nonlinear systems are studied in a linear algebraic framework. The general structure of left-inverse system is described and computed in symbolic algorithm. Two algorithms are given for constructing left-inverse systems with minimal order.展开更多
This paper gives a mathematical definition for the "caution" and "probing", and presents a decomposition theorem for nonlinear discrete-time stochastic systems. Under some assumptions, the problem ...This paper gives a mathematical definition for the "caution" and "probing", and presents a decomposition theorem for nonlinear discrete-time stochastic systems. Under some assumptions, the problem of finding the closed-loop optimal control can be decomposed into three problems: the deterministic optimal feedback, cautious optimal and probing optimal control problems.展开更多
This paper concerns the absolute stability problem of discrete-time descriptor systems with feedback connected ferromagnetic hysteresis nonlinearities. The ferromagnetic hysteresis model satisfies the passivity condit...This paper concerns the absolute stability problem of discrete-time descriptor systems with feedback connected ferromagnetic hysteresis nonlinearities. The ferromagnetic hysteresis model satisfies the passivity conditions of hysteresis operator, that is the input-output relation of the transformed operator is passive. The bound condition of the solution of the ferromagnetic hysteresis model is given. Through the framework of loop transformation, an augmented discrete-time descriptor system model is established for the stability analysis. A new extended Tsypkin criterion for the absolute stability of discrete-time descriptor systems with hysteresis is presented based on the linear matrix inequalities technique. A numerical example is given to illustrate the effectiveness of the extended criterion.展开更多
This paper addresses the problem of event-triggered finite-time H<sub>∞</sub> filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-K...This paper addresses the problem of event-triggered finite-time H<sub>∞</sub> filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H<sub>∞</sub> filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H<sub>∞</sub> filter gain matrices can be expressed in an explicit form.展开更多
An adaptive inverse controller for nonliear discrete-time system is proposed in this paper. A compound neural network is constructed to identify the nonlinear system, which includes a linear part to approximate the no...An adaptive inverse controller for nonliear discrete-time system is proposed in this paper. A compound neural network is constructed to identify the nonlinear system, which includes a linear part to approximate the nonlinear system and a recurrent neural network to minimize the difference between the linear model and the real nonlinear system. Because the current control input is not included in the input vector of recurrent neural network (RNN), the inverse control law can be calculated directly. This scheme can be used in real-time nonlinear single-input single-output (SISO) and multi-input multi-output (MIMO) system control with less computation work. Simulation studies have shown that this scheme is simple and affects good control accuracy and robustness.展开更多
Adaptive control of discrete-time parametric-strict-feedback nonlinear systems will be studied in this paper. To the best knowledge of the authors, almost all of the existing results for such systems need Lipschitz co...Adaptive control of discrete-time parametric-strict-feedback nonlinear systems will be studied in this paper. To the best knowledge of the authors, almost all of the existing results for such systems need Lipschitz condition. The main purpose of this paper is to take a step towards nonlinear growth rate for second-order systems. The control law is designed based on least squares （LS） algorithms and on recursive adaptive predictors. Global stability and tracking performance are established for the closed-loop systems.展开更多
基金This work is supported by the National Natural Science Foundation of China (No.60421002) Priority supported financially by the New Century 151 Talent Project of Zhejiang Province.
文摘A new variable structure control algorithm based on sliding mode prediction for a class of discrete-time nonlinear systems is presented. By employing a special model to predict future sliding mode value, and combining feedback correction and receding horizon optimization methods which are extensively applied on predictive control strategy, a discrete-time variable structure control law is constructed. The closed-loop systems are proved to have robustness to uncertainties with unspecified boundaries. Numerical simulation and pendulum experiment results illustrate that the closed-loop systems possess desired performance, such as strong robustness, fast convergence and chattering elimination.
文摘A new type criterion of globally uniformly ultimate boundedness for discrete-time nonlinear systems is introduced. In classical Lyapunov theory about globally uniformly ultimate boundedness, Lyapunov function is assumed to be positive definite and its difference at the every latter moment and the former moment is negative definite. In this paper the condition of difference of Lyapunov function is relaxed. Under the relaxed condition, the result of this paper can be considered as the extension of the classical Lyapunov theory about uniformly ultimate boundedness.
文摘In this paper, some computational tools are proposed to determine the largest invariant set, with respect to either a continuous-time or a discrete-time system, that is contained in an algebraic set. In particular, it is shown that if the vector field governing the dynamics of the system is polynomial and the considered analytic set is a variety, then algorithms from algebraic geometry can be used to solve the considered problem. Examples of applications of the method(spanning from the characterization of the stability to the computation of the zero dynamics) are given all throughout the paper.
基金Project (60425310) supported by the National Natural Science Foundation of China project (2001AA4422200) supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of the Ministry of Education of China
文摘The robustly asymptotical stability problem for discrete-time nonlinear systems with time-delay was investigated. Positive definite matrix are constructed through Lyapunov functional. With the identity transform, property of matrix inverse and S-procedure, a new sufficient condition independent of the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is established. With Schur complement, another equivalent sufficient condition for robust stability of discrete-time nonlinear systems with time-delay is given. Finally, a sufficient condition dependent on the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is obtained. A unified approach is used to cast the robust stability problem into a convex optimization involving linear matrix inequalities.
基金surported by Tianjin Science and Technology Development for Higher Education(20051206).
文摘An indirect adaptive fuzzy control scheme is developed for a class of nonlinear discrete-time systems. In this method, two fuzzy logic systems are used to approximate the unknown functions, and the parameters of membership functions in fuzzy logic systems are adjusted according to adaptive laws for the purpose of controlling the plant to track a reference trajectory. It is proved that the scheme can not only guarantee the boundedness of the input and output of the closed-loop system, but also make the tracking error converge to a small neighborhood of the origin. Simulation results indicate the effectiveness of this scheme.
文摘An uncertain nonlinear discrete-time system model with time-varying input delays for networked control systems (NCSs) is presented. The problem of exponential stability for the system is considered and some new criteria of exponential stability are obtained based on norm inequality methods. A numerical example is given todemonstrate that those criteria are useful to analyzing the stability of nonlinear NCSs.
基金supported by the National Natural Science Foundation of China(61074004)the Research Fund for the Doctoral Program of Higher Education(20110121110017)
文摘Transient performance for output regulation problems of linear discrete-time systems with input saturation is addressed by using the composite nonlinear feedback（CNF） control technique. The regulator is designed to be an additive combination of a linear regulator part and a nonlinear feedback part. The linear regulator part solves the regulation problem independently which produces a quick output response but large oscillations. The nonlinear feedback part with well-tuned parameters is introduced to improve the transient performance by smoothing the oscillatory convergence. It is shown that the introduction of the nonlinear feedback part does not change the solvability conditions of the linear discrete-time output regulation problem. The effectiveness of transient improvement is illustrated by a numeric example.
文摘This paper proposes a discrete-time robust control technique for an uncertain nonlinear system. The uncertainty mainly affects the system dynamics due to mismatched parameter variation which is bounded by a predefined known function. In order to compensate the effect of uncertainty, a robust control input is derived by formulating an equivalent optimal control problem for a virtual nominal system with a modified costfunctional. To derive the stabilizing control law for a mismatched system, this paper introduces another control input named as virtual input. This virtual input is not applied directly to stabilize the uncertain system, rather it is used to define a sufficient condition. To solve the nonlinear optimal control problem, a discretetime general Hamilton-Jacobi-Bellman(DT-GHJB) equation is considered and it is approximated numerically through a neural network(NN) implementation. The approximated solution of DTGHJB is used to compute the suboptimal control input for the virtual system. The suboptimal inputs for the virtual system ensure the asymptotic stability of the closed-loop uncertain system. A numerical example is illustrated with simulation results to prove the efficacy of the proposed control algorithm.
文摘This paper presents a robust sliding mode controller for a class of unknown nonlinear discrete-time systems in the presence of fixed time delay. A neural-network approximation and the Lyapunov-Krasovskii functional theory into the sliding-mode technique is used and a neural-network based sliding mode control scheme is proposed. Because of the novality of Chebyshev Neural Networks (CNNs), that it requires much less computation time as compare to multi layer neural network (MLNN), is preferred to approximate the unknown system functions. By means of linear matrix inequalities, a sufficient condition is derived to ensure the asymptotic stability such that the sliding mode dynamics is restricted to the defined sliding surface. The proposed sliding mode control technique guarantees the system state trajectory to the designed sliding surface. Finally, simulation results illustrate the main characteristics and performance of the proposed approach.
基金supported by the National High Technology Research and Development Program of China(863 Program)(2014AA06A503)the National Natural Science Foundation of China(61422307,61673361)+3 种基金the Scientific Research Starting Foundation for the Returned Overseas Chinese Scholars and Ministry of Education of Chinasupports from the Youth Top-notch Talent Support Programthe 1000-talent Youth Programthe Youth Yangtze River Scholarship
文摘In this paper,we studied the approximate sampleddata observer design for a class of stochastic nonlinear systems.Euler-Maruyama approximation was investigated in this paper because it is the basis of other higher precision numerical methods,and it preserves important structures of the nonlinear systems.Also,the form of Euler-Maruyama model is simple and easy to be calculated.The results provide a reference for sampled-data observer design method for such stochastic nonlinear systems,and may be useful to many practical control applications,such as tracking control in mechanical systems.And the effectiveness of the approach is demonstrated by a simulation example.
文摘This paper discusses about the stabilization of unknown nonlinear discrete-time fixed state delay systems. The unknown system nonlinearity is approximated by Chebyshev neural network (CNN), and weight update law is presented for approximating the system nonlinearity. Using appropriate Lyapunov-Krasovskii functional the stability of the nonlinear system is ensured by the solution of linear matrix inequalities. Finally, a relevant example is given to illustrate the effectiveness of the proposed control scheme.
基金supported by the National Natural Science Foundation of China(61573129 U1804147)+2 种基金the Innovative Scientists and Technicians Team of Henan Provincial High Education(20IRTSTHN019)the Innovative Scientists and Technicians Team of Henan Polytechnic University(T2019-2 T2017-1)
文摘An event-triggered scheme is proposed to solve the problems of robust guaranteed cost control for a class of two-dimensional(2-D)discrete-time systems.Firstly,an eventtriggered scheme is proposed for 2-D discrete-time systems with parameter uncertainties and sector nonlinearities.Then,according to the Lyapunov functional method,the sufficient conditions for the existence of event-triggered robust guaranteed cost controller for 2-D discrete-time systems with parameter uncertainties and sector nonlinearities are given.Furthermore,based on the sufficient conditions and the linear matrix inequality(LMI)technique,the problem of designing event-triggered robust guaranteed cost controller is transformed into a feasible solution problem of LMI.Finally,a numerical example is given to demonstrate that,under the proposed event-triggered robust guaranteed cost control,the closed-loop system is asymptotically stable and fewer communication resources are occupied.
文摘In this paper, a computational approach is proposed for solving the discrete-time nonlinear optimal control problem, which is disturbed by a sequence of random noises. Because of the exact solution of such optimal control problem is impossible to be obtained, estimating the state dynamics is currently required. Here, it is assumed that the output can be measured from the real plant process. In our approach, the state mean propagation is applied in order to construct a linear model-based optimal control problem, where the model output is measureable. On this basis, an output error, which takes into account the differences between the real output and the model output, is defined. Then, this output error is minimized by applying the stochastic approximation approach. During the computation procedure, the stochastic gradient is established, so as the optimal solution of the model used can be updated iteratively. Once the convergence is achieved, the iterative solution approximates to the true optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, an example on a continuous stirred-tank reactor problem is studied, and the result obtained shows the applicability of the approach proposed. Hence, the efficiency of the approach proposed is highly recommended.
基金supported in part by National Natural Science Foundation of China(Grant Nos.6137410561233001+1 种基金61273140)in part by Beijing Natural Science Foundation(Grant No.4132078)
文摘In this paper, a novel iterative Q-learning algorithm, called "policy iteration based deterministic Qlearning algorithm", is developed to solve the optimal control problems for discrete-time deterministic nonlinear systems. The idea is to use an iterative adaptive dynamic programming(ADP) technique to construct the iterative control law which optimizes the iterative Q function. When the optimal Q function is obtained, the optimal control law can be achieved by directly minimizing the optimal Q function, where the mathematical model of the system is not necessary. Convergence property is analyzed to show that the iterative Q function is monotonically non-increasing and converges to the solution of the optimality equation. It is also proven that any of the iterative control laws is a stable control law. Neural networks are employed to implement the policy iteration based deterministic Q-learning algorithm, by approximating the iterative Q function and the iterative control law, respectively. Finally, two simulation examples are presented to illustrate the performance of the developed algorithm.
文摘The left-inverse system with minimal order and its algorithms of discrete-time nonlinear systems are studied in a linear algebraic framework. The general structure of left-inverse system is described and computed in symbolic algorithm. Two algorithms are given for constructing left-inverse systems with minimal order.
文摘This paper gives a mathematical definition for the "caution" and "probing", and presents a decomposition theorem for nonlinear discrete-time stochastic systems. Under some assumptions, the problem of finding the closed-loop optimal control can be decomposed into three problems: the deterministic optimal feedback, cautious optimal and probing optimal control problems.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 50977008,60821063 and 61034005)National Basic Research Program of China (Grant No. 2009CB32060)
文摘This paper concerns the absolute stability problem of discrete-time descriptor systems with feedback connected ferromagnetic hysteresis nonlinearities. The ferromagnetic hysteresis model satisfies the passivity conditions of hysteresis operator, that is the input-output relation of the transformed operator is passive. The bound condition of the solution of the ferromagnetic hysteresis model is given. Through the framework of loop transformation, an augmented discrete-time descriptor system model is established for the stability analysis. A new extended Tsypkin criterion for the absolute stability of discrete-time descriptor systems with hysteresis is presented based on the linear matrix inequalities technique. A numerical example is given to illustrate the effectiveness of the extended criterion.
文摘This paper addresses the problem of event-triggered finite-time H<sub>∞</sub> filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H<sub>∞</sub> filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H<sub>∞</sub> filter gain matrices can be expressed in an explicit form.
基金Supported by the National Natural Science Foundation of China (60575009, 60574036)
文摘An adaptive inverse controller for nonliear discrete-time system is proposed in this paper. A compound neural network is constructed to identify the nonlinear system, which includes a linear part to approximate the nonlinear system and a recurrent neural network to minimize the difference between the linear model and the real nonlinear system. Because the current control input is not included in the input vector of recurrent neural network (RNN), the inverse control law can be calculated directly. This scheme can be used in real-time nonlinear single-input single-output (SISO) and multi-input multi-output (MIMO) system control with less computation work. Simulation studies have shown that this scheme is simple and affects good control accuracy and robustness.
基金the National Natural Science Foundation of China (Grant Nos. 60204010 and 60474499)the Aviation Foundation of China(Grant No. 00E51083)
文摘Adaptive control of discrete-time parametric-strict-feedback nonlinear systems will be studied in this paper. To the best knowledge of the authors, almost all of the existing results for such systems need Lipschitz condition. The main purpose of this paper is to take a step towards nonlinear growth rate for second-order systems. The control law is designed based on least squares （LS） algorithms and on recursive adaptive predictors. Global stability and tracking performance are established for the closed-loop systems.
