Research On Robust And Non-fragile Control Method For Markov Jump Systems With Partly Known Probabilities

Markov jump system(MJS)is a special kind of stochastic switching system including two parts:finite discrete jump modes and continuous states which are governed by Markov process and differential equations,respectively.It has strong modeling capabilities for the actual systems with random changing structure or parameters.Recent years,much attention has been attracted to this field.It is research results have been widely used in such system as power system,manufacturing system,flight system and so on.The main object is to make full use of the information of measurable premise variables,to obtain less conservative results and to improve the tracking performance.In addition,in the actual production process,digital circuit has been widely applied for its simple structure and software support mechanism,but due to the influence of finite word length and sampling frequency,there will always be perturbations in the actual controller.It has been proved that the controller designed by the traditional optimal and robust controller design is fragile,that is,the tiny perturbation in the controller will seriously affect the performance of the system.It is well known that disturbances exist in most practical controlled processes,due to the friction and load variation in mechanical and electrical systems,measurement noises,environment disturbance,the errors caused by sensors and actuators,and so on.Hence,to guarantee the stability and pursue performances,how to attenuate and reject the disturbances,especially.for the nonlinear systems,becomes a crucial problem.Chapters 1-2 the background and the basic concepts of the Markov jump system are introduced.Then the relevant basic knowledge of mathematics is given.In the Chapter 3,a robust non-fragile controller is designed for the Markov jump linear system with general transition probabilities.Numerical examples are used to verify the effectiveness of the method.In the Chapter 4,the problem of disturbance-observer-based-control(DOBC)and L2-L? non-fragile control for Markovian jump non-linear systems with multiple disturbances is investigated.The basic idea of the DOBC scheme is to construct an observer to estimate the disturbance,and then based on the output of the observer,a feedforward compensator plus conventional control laws are applied to rej ect the disturbance,and achieve the desired performance.A numerical example and a practical example are used to verify the effectiveness of the method.Chapter 5 investigates the design of robust nonfragile controller for the Markov jump system with polytopic-type parameter uncertainty.The effectiveness of the method is verified through simulation.At last,conclusions and further research directions are given in the sixth chapter.