High-dispersion Temporal Stabilization And Tracking Control Of Stochastic System

Due to the inevitable influence of noise on real systems,the stabilization control of stochastic systems has received widespread attention in the past few decades.Traditional feedback control based on continuous-time state observation is costly and even difficult to implement.Therefore,the stabilization control based on discrete-time state observation has been a research focus in the past decade.This paper studies the discrete-time feedback stabilization of four types of stochastic systems.In addition,the tracking control is a more practical problem closely related to stabilization control.Therefore,this paper also makes a preliminary exploration on the tracking control of high-order stochastic time-delay systems.This paper is divided into eight chapters:Chapter 1 explains the research background,reviews the research status,describes the research motivation,and gives the framework of the paper.Chapter 2 explains the basic theory and symbols.Chapter 3 studies stochastic non-autonomous systems.The results show that although the coefficients of the underlying system do not have a uniform lower bound,they can be almost sure polynomial stabilization through discrete-time feedback control.Chapter 4 studies stochastic second-order systems.By attaching different discrete-time controllers to the two subsystems of the second-order system,this chapter achieves different kinds of stabilization for the two subsystems.Chapter 5 studies hybrid stochastic time-delay systems.The method of Lyapunov functional and auxiliary system are combined in this chapter to study the effects of time-delay and discrete-time state observation,respectively.In order to illustrate the effectiveness of the proposed controller design scheme,a numerical example is also given at the end of this chapter.Chapter 6 studies stochastic hybrid systems driven by Levy processes.In this chapter,by constructing Lyapunov function and utilizing the properties of Poisson compensated martingale measure,discrete-time stabilization in distribution of the underlying system is achieved.In Chapter 7,theoretical analysis of tracking control for high-order stochastic time-delay systems with stochastic inverse dynamics is achieved using the adding-a-power integrator method and the design of Lyapunov-Krasovskii function.Finally,Chapter 8 summarizes and self-evaluates the work done in this paper,and makes a plan for the next research to a certain extent.