Adaptive Control Of Uncertain System With Delays And Nonlinear System

Based on the Lyapunov stability theory,this dissertation is mainly on the design of the robust adaptive controllers for uncertain time delay systems subject to different assumptions by using linear matrix inequalities(LMIs),and the design of the adaptive control of a class of nonlinear discrete-time systems by the use of least square support vector machine algorithm (LSSVM).The main work of this dissertation consists of six parts as follows:In part one,the research development and general situation about the adaptive control for time delay systems are discussed first,and then the main mathematical tools and methods, which will be used in this dissertation,are stated.Furthermore,the main problems,which are studied in this dissertation,are introduced.Finally,some necessary preliminaries in this dissertation are given.In part two,the problem of robust adaptive controller design for two classes of uncertain time varying delay systems is studied.First,the problem of robust adaptive stabilization for a class of multiple time-delay uncertain systems is discussed.The time-delay uncertainties are assumed to satisfy the mismatching conditions and the values of its upper bounds are unknown.By using of the LMI and Lyapunov-Krosovskii functional we propose a memoryless adaptive state feedback controller,which can guarantee the closed-loop system is globally stable in the sense of uniform ultimate boundedness.Finally,the problem of adaptive stabilization for a class of nonlinear systems including matching time-varying delayed disturbance is discussed.The bound of the time-varying delayed state disturbances are unknown and are assumed to satisfy the linear growth conditions.By using of the Lyapunov stability theory and Lyapunov-Krosovskii functional we propose a robust adaptive state feedback controller,which can guarantee the closed-loop system is globally stable in the sense of uniform ultimate boundedness and the state trajectories are uniformly asymptotically to zero.In part three,the problem of decentralized robust adaptive control is considered for a class of uncertain large-scale time-delay systems in the presence of mismatched and matched uncertainties.The constant time delay is considered first.The interconnections are assumed to be bounded by a linear function of delayed states with unknown gains.The upper bounds of the matching uncertainties and perturbations are also assumed to be unknown.The adaptation laws are proposed to estimate such unknown bounds,and by making use of the LMI method,a class of decentralized robust adaptive controllers is constructed.Based on the Lyapunov stability theory and Lyapunov-Krasovskii functional,it is shown that the state trajectories of the large-scale systems are uniformly asymptotically to zero.Then the above results are extended to the situation with time varying delay.Different decentralized adaptive controllers are designed for time varying delay subject to different conditions.Satisfactory results are also achieved.In part four,the problem of adaptive output feedback stabilization control for uncertain time varying delay systems is studied.A class of uncertain dynamic system including time-varying delayed perturbations is discussed first.The uncertainties are assumed to satisfy the so-called matching conditions and the transfer function matrix of the nominal system is strictly feedback positive real.By using of the Lyapunov stability theory and Lyapunov-Krosovskii functional we propose two different output feedback adaptive controllers and two different adaptation laws to estimate the unknown upper bounds of the uncertainties of the system,which all can guarantee the closed-loop system is globally stable in the sense of uniform ultimate boundedness.In addition,one of them can guarantee the state trajectories of the system are uniformly asymptotically to zero.Then the problem of decentralized adaptive output feedback stabilization for a class of large-scale systems subject to uncertain parameters and multiple time-varying delays in the interconnections is studied. The interconnections are assumed to satisfy the matching conditions and the nominal system of each subsystems is strictly feedback positive real.By estimating the unknown bounds of the uncertain parameter matrices we propose an decentralized output feedback adaptive controller, which can guarantee the closed-loop system to converge,globally,uniformly and exponentially,to a bounded ball.In part five,the problem of adaptive sliding mode control for time varying delay systems is studied.A class of time varying delay systems with mismatched uncertainties and matched external perturbations is investigated first.Based on the Lyapunov theory,a sufficient condition derived in terms of LMI is given to guarantee the existence of the sliding surface. The adaptive control is used to overcome the unknown upper bound of perturbations.The globally asymptotic stability is also achieved for the proposed control methodology.Then the adaptive sliding mode control scheme with saturation actuator is considered.The approach not only removes the assumption that the bounds of the saturation are known,but also give the existence and reachable conditions of the sliding-mode.By theoretical analysis,it is shown that the asymptotical stability of the closed-loop system is guaranteed under the saturation input.Finally,the problem of robust tracking and model following is considered for a class of linear large-scale systems subject to time varying delay interconnections and external disturbances.Based on the Lyapunov stability theory,a decentralized adaptive sliding mode control scheme is proposed.An adaptation algorithm that can adapt the unknown upper bounds of the uncertainties and time varying delay interconnections is introduced as well as integral sliding mode,so that the tracking error decrease asymptotically to zero and reference model following is achieved.Finally,we introduce the use of recurrent least square support vector machine algorithm for the adaptive control of a class of nonlinear discrete-time systems.Comparing to neural networks,the regression support vector machines with one or more hidden layer not only can approximate any nonlinear function on the compact set but also has well generalization ability and the ability to adaptively determine the complexity of the model.The procedure is finally comes down to solve a set of linear equations in an iterative way.Advantage of the newly designed algorithm is that the computation of inverse matrix is avoided.The curse of dimensionality is also avoided by using the finite time window.In this dissertation,simulations are made for major design schemes.Simulation results also show the effectiveness of the proposed approaches.