T-S Fuzzy Control And Event-Triggered Control For Stochastic Nonlinear Uncertain Systems

In practical applications,real systems,may experience a sudden change in their parameters and structure and may experience stochastic disturbances,which cause adverse effect on the performance of the control system,and even lead to system instability,so the investigation on stability analysis and a variety of control methods of stochastic nonlinear system with Markov jump parameters has received increasing attention.This dissertation mainly investigates a class of stochastic nonlinear uncertain systems with Markov jump parameters with the help of Takagi-Sugeno fuzzy control strategy and event-triggered strategy.The main works of this study are:1.The problem of robust nonfragile guaranteed cost control for uncertain discrete-time T–S fuzzy systems with Markov jump parameters and time-varying delay is investigated.A nonfragile fuzzy-basis-dependent and mode-dependent controller is designed and a sufficient condition is developed to ensure that the resulting closed-loop system is robust asymptotically stable in mean square with guaranteed cost index not exceeding the specified upper bound.Subsequently,the optimal controller gain and optimal upper bound of the performance cost can be obtained by solving the optimization problem.Compared with the existing literature,this method enormously reduces the conservatism of the existing results.Finally,numerical and practical examples are provided to demonstrate the performance of the proposed approach.2.The problem of nonfragile guaranteed cost control for uncertain T–S fuzzy systems with Markov jump parameters and time-varying delay is investigated.A nonfragile modedependent fuzzy controller is designed and a weak sufficient condition is developed to ensure that the resulting closed-loop system is robust almost surely asymptotically stable with guaranteed cost index not exceeding the specified upper bound.Subsequently,the controller gain and upper bound of the guaranteed cost index can be obtained by solving a set of linear matrix inequalities.The method proposed can effectively reduce the conservatism of the results obtained and the upper bound of the cost index,compared with the [91],as well as the control amplitude can be reduced.Finally,numerical and practical examples of the single-link robot arm system are provided to demonstrate the performance of the proposed approach.3.The problem of robust nonfragile guaranteed cost control for uncertain T-S fuzzy systems with Markov jump parameters,time-varying delay and input constraint is investigated.A sufficient condition is developed to ensure that the resulting closed-loop system is robust almost surely asymptotically stable with guaranteed cost index not exceeding the specified upper bound.By designing a nonfragile mode-dependent average dwell time fuzzy controller with input constraint,the upper bound of the guaranteed cost controller index and the conservatism of the results obtained can be enormously decreased and meanwhile the control amplitude can be kept within an appropriate bound.Subsequently,the controller gain and upper bound of the guaranteed cost index can be obtained by solving a set of linear matrix inequalities.Finally,numerical and practical examples are provided to demonstrate the performance of the proposed approach.4.The problem of event-triggered adaptive tracking control for a class of stochastic nonlinear systems with Markov jump parameters is investigated.Since the stochastic system contains unknown parameters,the assumption of the stochastic input-to-state stability is a difficult task to check.To overcome the design difficulty,mode-dependent adaptive controllers and the event-triggered strategy are designed simultaneously with the help of backstepping technique.The stochastic input-to-state stability assumption is avoided by adding correction terms in controller to compensate the measurement errors.The proposed control schemes guarantee that all signals in the closed-loop system remain bounded in probability,the tracking error signals eventually converge to the compact set in the sense of mean quartic value and the Zeno behavior is successfully avoided.Finally,simulation results show the effectiveness of the proposed approach.5.The adaptive dynamic surface prescribed performance control for stochastic Markov jump systems based on event-triggered method is investigated.Using the backstepping method,we propose two adaptive dynamic surface controllers with average dwell time and the event-triggered strategies simultaneously.The existed assumption of stochastic input-tostate stability on the stochastic systems can be avoided by adding a correction terms into the controller to compensate for the measurement error.The method designed can make all signals in the closed-loop stochastic Markov jump nonlinear uncertain system remain bounded in probability,the tracking error signals eventually converge to the compact set with the prescribed performance bound in the sense of mean quartic value and the Zeno behavior is successfully avoided.Furthermore,the designed even-driven relative threshold strategy which relies on the control signal reduces the frequency of events triggered.Finally,the validity of put forward method is shown in simulation results.