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Research On Robust Control And Filter For Infinite Markov Jump Systems

Posted on:2020-05-04Degree:DoctorType:Dissertation
Country:ChinaCandidate:Y Y LiuFull Text:PDF
GTID:1488306032461524Subject:Systems science, systems analysis and integration
Abstract/Summary:PDF Full Text Request
It is well known that Markov jump systems have been widely used in the fields of economic systems,network communication systems and biological systems.As a special hybrid system,Markov jump systems have always been the research object of people's attention.Markov jump systems with multiplicative noise have been successfully used to study a large variety of problems in many fields,ranging from stability,robust control to filtering.However,most of the existing literatures focused on exploring the case where the Markov chain takes values in a finite state space.In fact,it may be more appropriate to characterize some physical phenomena in real world via an infinite-state Markov chain.Therefore,in order to describe the actual systems more accurately,stochastic systems with infinite Markov jump systems are considered in the model of the actual systems.Under the assumption that the state space of Markov chain is countablely infinite set,the results of control theory are very limited,and some important problems of analysis and design problems have not been deeply studied.Based on this,in this paper,the robust control and filter problems for infinite Markov jump stochastic systems have been investigated.Around this center,the main works of this paper are as follows:1.The infinite horizon H2/H? control problem for discrete-time infinite Markov jump stochastic systems is studied.Under the conditions of exponential stabilization and strong detectability,the linear quadratic control problem of discrete-time infinite Markov jump stochastic systems is discussed,and it is proved that the existence of the infinite horizon mixed H2/H? control is equivalent to the solvability of the generalized coupled matrix Riccati equations.Then,a backward iteration algorithm is proposed to solve the generalized coupled matrix Riccati equations,further,the optimal H2/H? controller is obtained by using this algorithm.2.The H2/H? control problem for continuous-time infinite Markov jump stochastic systems is studied.Based on the method of refutation,a new method for proving linear quadratic problem of time-varying stochastic systems is proposed,stochastic bounded real lemma is established and the finite horizon mixed H2/H? controller is obtained by means of the generalized coupled differential Riccati equations.Further,we consider infinite horizon linear quadratic Nash games for time-invariant systems.As an important application,the infinite horizon mixed H2/H? control problem is investigated by Nash game approach,and the relationship between the Nash game and the infinite horizon mixed H2/H? control problem is disscussed when the disturbance does or does not enter into the diffusion term.The backward iteration algorithm of solving the generalized coupled algebraic Riccati equations is given by using the discretization method and the asymptotic analysis properties of the generalized coupled differential Riccati equations.Because the process of solving Riccati equations is complicated,the improved genetic algorithm is proposed to design the optimal H2/H? controller.3.Exponential stability and H? control problem are investigated for discrete-time stochastic system with infinite Markov jump and time-delay.By introducing a novel Lyapunov-Krasovskii functional,a state feedback controller is designed to guarantee that the discrete-time stochastic system with infinite Markov jump and time-delay is mean square exponential stability and satisfies a prescribed H? performance level.Moreover,based on the uncertainty of system parameters,the exponential stability criterion for uncertain discrete-time infinite Markov jump stochastic systems with time-delay is obtained.On this basis,the relationship between asymptotic mean square stability,stochastic stability,exponential mean square stability and exponential mean square stability with conditioning are further discussed,and the equivalence among four stabilities is given by sufficient condition.At last,the effectiveness of the proposed design method is verified by simulation results.4.The filtering problem for nonlinear stochastic systems with infinite Markov jump is studied.A sufficient condition for the existence of infinite horizon control for nonlinear stochastic systems with infinite Markov jump is given by coupled Hamilton-Jacobi inequalities.Based on T-S fuzzy model and linear matrix inequalities,exponentially mean square stable filter with a prescribed H? performance level is given.When we consider the worst disturbance,suboptimal H2/H? fuzzy filtering is designed by minimizing the estimation error energy.Some simulation results are given to illustrate the usefulness of the proposed design method.
Keywords/Search Tags:Infinite Markov jump systems, Exponential stability, Robust control, Filtering, Generalized coupled Riccati equations
PDF Full Text Request
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