The optimal control problem with a long run average cost is investigated for unknown linear discrete-time systems with additive noise.The authors propose a value iteration-based stochastic adaptive dynamic programming...The optimal control problem with a long run average cost is investigated for unknown linear discrete-time systems with additive noise.The authors propose a value iteration-based stochastic adaptive dynamic programming(VI-based SADP)algorithm,based on which the optimal controller is obtained.Different from the existing relevant work,the algorithm does not need to estimate the expectation(conditional expectation)and variance(conditional variance)of states or other relevant variables,and the convergence of the algorithm can be proved rigorously.A simulation example is given to verify the effectiveness of the proposed approach.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
The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system (DFBS) is presented. Based on parallel distribution compensation method, some sufficient conditions are de...The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system (DFBS) is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality (LMI) so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.展开更多
In this correspondence paper, an equivalent stability criterion with minimal number of linear matrix inequality (LMI) variables is presented for a delay-dependent stability criterion reported recently in the Interna...In this correspondence paper, an equivalent stability criterion with minimal number of linear matrix inequality (LMI) variables is presented for a delay-dependent stability criterion reported recently in the International Journal of Automation and Computing for a class of linear discrete-time systems with additive time delays. The reported stability criterion for the additive timedelay systems has more number of matrix variables in the LMI and, hence, demand additional computational burden. The proposed equivalent stability criterion, unlike the reported one, does not involve free-weighing matrices and encompass only the matrix variables that are associated in the Lyapunov-Krasovskii functional, making the criterion mathematically less complex and computationally more effective.展开更多
The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear...The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.展开更多
This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties. A new and simple method is presented to directly decouple the Lyapunov matrix ...This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties. A new and simple method is presented to directly decouple the Lyapunov matrix and the system dynamic matrix. Combining this method with the parameter-dependent Lyapunov function approach yields new criteria that include some existing ones as special cases. A numerical example illustrates the improvement over the existing ones.展开更多
In this paper, stability of discrete-time linear systems subject to actuator saturation is analyzed by combining the saturation-dependent Lyapunov function method with Finsler’s lemma. New stability test conditions a...In this paper, stability of discrete-time linear systems subject to actuator saturation is analyzed by combining the saturation-dependent Lyapunov function method with Finsler’s lemma. New stability test conditions are proposed in the enlarged space containing both the state and its time difference which allow extra degree of freedom and lead to less conservative estimation of the domain of attraction. Furthermore, based on this result, a useful lemma and an iterative LMI-based optimization algorithm are also developed to maximize an estimation of domain of attraction. A numerical example illustrates the effectiveness of the proposed methods.展开更多
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
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
This paper studies deterministic and stochastic fixedtime stability of autonomous nonlinear discrete-time(DT)systems.Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT sys...This paper studies deterministic and stochastic fixedtime stability of autonomous nonlinear discrete-time(DT)systems.Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT systems is certified.Extensions to systems under deterministic perturbations as well as stochastic noise are then considered.For the former,sensitivity to perturbations for fixed-time stable DT systems is analyzed,and it is shown that fixed-time attractiveness results from the presented Lyapunov conditions.For the latter,sufficient Lyapunov conditions for fixed-time stability in probability of nonlinear stochastic DT systems are presented.The fixed upper bound of the settling-time function is derived for both fixed-time stable and fixed-time attractive systems,and a stochastic settling-time function fixed upper bound is derived for stochastic DT systems.Illustrative examples are given along with simulation results to verify the introduced results.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
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 focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems(DFBS).Based on the parallel distributed compensation(PDC) approach,the sufficient co...This paper focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems(DFBS).Based on the parallel distributed compensation(PDC) approach,the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the cost function value is no more than a certain upper bound in the presence of the additive controller gain perturbations.The non-fragile guaranteed cost controller can be obtained by solving a set of bilinear matrix inequalities(BMIs).The Van de Vusse model is utilized to demonstrate the validity and effectiveness of the proposed approach.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
The robust reliable H∞ control problem for discrete-time Markovian jump systems with actuator failures is studied. A more practical model of actuator failures than outage is considered. Based on the state feedback me...The robust reliable H∞ control problem for discrete-time Markovian jump systems with actuator failures is studied. A more practical model of actuator failures than outage is considered. Based on the state feedback method, the resulting closed-loop systems are reliable in that they remain robust stochastically stable and satisfy a certain level of H∞ disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures, The solvability condition of controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities (LMIs). A numerical example is also given to illustrate the design procedures and their effectiveness.展开更多
Formation control of discrete-time linear multi-agent systems using directed switching topology is considered in this work via a reduced-order observer, in which a formation control protocol is proposed under the assu...Formation control of discrete-time linear multi-agent systems using directed switching topology is considered in this work via a reduced-order observer, in which a formation control protocol is proposed under the assumption that each directed communication topology has a directed spanning tree. By utilizing the relative outputs of neighboring agents, a reduced-order observer is designed for each following agent. A multi-step control algorithm is established based on the Lyapunov method and the modified discrete-time algebraic Riccati equation. A sufficient condition is given to ensure that the discrete-time linear multi-agent system can achieve the expected leader-following formation.Finally, numerical examples are provided so as to demonstrate the effectiveness of the obtained results.展开更多
Recently, the robust output regulation problem for continuous-time linear systems with both input and communication time-delays was studied. This paper will further present the results on the robust output regulation ...Recently, the robust output regulation problem for continuous-time linear systems with both input and communication time-delays was studied. This paper will further present the results on the robust output regulation problem for discrete-time linear systems with input and communication delays. The motivation of this paper comes from two aspects. First, it is known that the solvability of the output regulation problem for linear systems is dictated by two matrix equations. While, for delay-free systems, these two matrix equations are same for both continuous-time systems and discretetime systems, they are different for continuous-time time-delay systems and discrete-time time-delay systems. Second, the stabilization methods for continuous-time time-delay systems and discrete-time time-delay systems are also somehow different. Thus, an independent treatment of the robust output regulation problem for discrete-time time-delay systems will be useful and necessary.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
基金supported by the National Natural Science Foundation of China under Grant No.61673284the Science Development Project of Sichuan University under Grant No.2020SCUNL201。
文摘The optimal control problem with a long run average cost is investigated for unknown linear discrete-time systems with additive noise.The authors propose a value iteration-based stochastic adaptive dynamic programming(VI-based SADP)algorithm,based on which the optimal controller is obtained.Different from the existing relevant work,the algorithm does not need to estimate the expectation(conditional expectation)and variance(conditional variance)of states or other relevant variables,and the convergence of the algorithm can be proved rigorously.A simulation example is given to verify the effectiveness of the proposed approach.
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.
文摘The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system (DFBS) is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality (LMI) so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.
文摘In this correspondence paper, an equivalent stability criterion with minimal number of linear matrix inequality (LMI) variables is presented for a delay-dependent stability criterion reported recently in the International Journal of Automation and Computing for a class of linear discrete-time systems with additive time delays. The reported stability criterion for the additive timedelay systems has more number of matrix variables in the LMI and, hence, demand additional computational burden. The proposed equivalent stability criterion, unlike the reported one, does not involve free-weighing matrices and encompass only the matrix variables that are associated in the Lyapunov-Krasovskii functional, making the criterion mathematically less complex and computationally more effective.
基金Supported by the State Key Program of National Natural Science of China (60534010), National Basic Research Program of China (973 Program)(2009CB320604), National Natural Science Foundation of China (60674021), the Funds for Creative Research Groups of China (60521003), the 111 Project(B08015), and the Funds of Ph.D. Program of Ministry of Eduction, China (20060145019).
基金This work was partially supported by RGC Grant 7103/01P and the open project of the state key Laboratory of intelligent and Systems,Tsinghua University(No.0406).
文摘The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.
基金This work was supported in part by the Doctor Subject Foundation of China (No. 20050533015)the National Science Foundation of China(No. 60425310,60574014).
文摘This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties. A new and simple method is presented to directly decouple the Lyapunov matrix and the system dynamic matrix. Combining this method with the parameter-dependent Lyapunov function approach yields new criteria that include some existing ones as special cases. A numerical example illustrates the improvement over the existing ones.
基金supported by Program for New Century Excellent Talents in University (No.NCET-04-0283)the Funds for Creative Research Groups of China (No.60521003)+4 种基金Program for Changjiang Scholars and Innovative Research Team in University (No.IRT0421)the State Key Programof National Natural Science of China (No.60534010)the Funds of National Science of China (No.60674021)the Funds of PhD program of MOE,China (No.20060145019)the 111 Project (No.B08015)
文摘In this paper, stability of discrete-time linear systems subject to actuator saturation is analyzed by combining the saturation-dependent Lyapunov function method with Finsler’s lemma. New stability test conditions are proposed in the enlarged space containing both the state and its time difference which allow extra degree of freedom and lead to less conservative estimation of the domain of attraction. Furthermore, based on this result, a useful lemma and an iterative LMI-based optimization algorithm are also developed to maximize an estimation of domain of attraction. A numerical example illustrates the effectiveness of the proposed methods.
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This work relates to Department of Navy award N00014-22-1-2159 issued by the Office of Naval Research。
文摘This paper studies deterministic and stochastic fixedtime stability of autonomous nonlinear discrete-time(DT)systems.Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT systems is certified.Extensions to systems under deterministic perturbations as well as stochastic noise are then considered.For the former,sensitivity to perturbations for fixed-time stable DT systems is analyzed,and it is shown that fixed-time attractiveness results from the presented Lyapunov conditions.For the latter,sufficient Lyapunov conditions for fixed-time stability in probability of nonlinear stochastic DT systems are presented.The fixed upper bound of the settling-time function is derived for both fixed-time stable and fixed-time attractive systems,and a stochastic settling-time function fixed upper bound is derived for stochastic DT systems.Illustrative examples are given along with simulation results to verify the introduced results.
基金Supported by National Basic Research Program of China (973 Program) (2009CB320604), State Key Program of National Natural Science Foundation of China (60534010), National Natural Science Foundation of China (60674021), Funds for Creative Research Groups of China (60821063), the 111 Project (B08015), and the Funds of Doctoral Program of Ministry of Education of China (20060145019)
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.
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.
基金supported by the National Natural Science Foundation of China(60374015)
文摘This paper focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems(DFBS).Based on the parallel distributed compensation(PDC) approach,the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the cost function value is no more than a certain upper bound in the presence of the additive controller gain perturbations.The non-fragile guaranteed cost controller can be obtained by solving a set of bilinear matrix inequalities(BMIs).The Van de Vusse model is utilized to demonstrate the validity and effectiveness of the proposed approach.
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the National Natural Science Foundation of China (60574001)Program for New Century Excellent Talents in University (05-0485)Program for Innovative Research Team of Jiangnan University
文摘The robust reliable H∞ control problem for discrete-time Markovian jump systems with actuator failures is studied. A more practical model of actuator failures than outage is considered. Based on the state feedback method, the resulting closed-loop systems are reliable in that they remain robust stochastically stable and satisfy a certain level of H∞ disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures, The solvability condition of controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities (LMIs). A numerical example is also given to illustrate the design procedures and their effectiveness.
基金supported by National Natural Science Foundation of China(61573200,61973175)the Fundamental Research Funds for the Central Universities,Nankai University(63201196)。
文摘Formation control of discrete-time linear multi-agent systems using directed switching topology is considered in this work via a reduced-order observer, in which a formation control protocol is proposed under the assumption that each directed communication topology has a directed spanning tree. By utilizing the relative outputs of neighboring agents, a reduced-order observer is designed for each following agent. A multi-step control algorithm is established based on the Lyapunov method and the modified discrete-time algebraic Riccati equation. A sufficient condition is given to ensure that the discrete-time linear multi-agent system can achieve the expected leader-following formation.Finally, numerical examples are provided so as to demonstrate the effectiveness of the obtained results.
基金supported by the Research Grants Council of the Hong Kong Special Administration Region under Grant No.412813
文摘Recently, the robust output regulation problem for continuous-time linear systems with both input and communication time-delays was studied. This paper will further present the results on the robust output regulation problem for discrete-time linear systems with input and communication delays. The motivation of this paper comes from two aspects. First, it is known that the solvability of the output regulation problem for linear systems is dictated by two matrix equations. While, for delay-free systems, these two matrix equations are same for both continuous-time systems and discretetime systems, they are different for continuous-time time-delay systems and discrete-time time-delay systems. Second, the stabilization methods for continuous-time time-delay systems and discrete-time time-delay systems are also somehow different. Thus, an independent treatment of the robust output regulation problem for discrete-time time-delay systems will be useful and necessary.
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.