Stability Analysis And Control Of Some Classes Of Nonlinear Stochastic/random Systems

As an important part of nonlinear systems,nonlinear stochastic/random systems take into account various types of environmental noises,and come to play an important role in many branches of science and industry.Due to the factors of stochastic disturbances,it becomes much more complicated and difficult to analyze and control them compared with the deterministic cases.Therefore,the study of stability analysis and controller design for nonlinear stochastic/random systems is very important from the point of control theory and practical application.In this dissertation,the controller design and stability analysis problems are investigated and addressed for several classes of important nonlinear stochastic/random systems by us-ing time-varying control approach,stochastic LaSalle-type theorem,stochastic Lyapunov-Krasovskii functional and multiple Lyapunov functions technique.The effective control strategy and the novel stability criteria are proposed.The main contributions of this thesis include:1.For a class of stochastic upper triangular nonlinear systems with an unknown growth rate,the time-varying state feedback stabilization problem is considered.To begin with,a LaSalle-type theorem for stochastic time-varying systems is established by using the generalized weakly positive definite function.To deal with serious uncertainties in the unknown growth rate,a time-varying approach,rather than an adaptive one,is adopted to design the scheme of a state feedback controller for stochastic feedforward systems.Based on the established LaSalle-type theorem,it is easily shown that all signals of the resulting closed-loop system converge to zero almost surely.2.The problem of decentralized stabilization for a class of large-scale stochastic high-order time-delay upper triangular nonlinear systems is studied.A series of delay-independent state feedback controllers is constructed,which is based on the approaches of adding one power integrator and Backstepping design.The stochastically global asymptotic stabil-ity of the closed-loop system under the mentioned controllers is proved by Lyapunov-Krasovskii theorem.A simulation example is given to illustrate the effectiveness of the proposed method.3.For a class of large-scale stochastic time-delay nonlinear systems,the decentralized out-put feedback stabilization problem is dealt with.Firstly,a filter is proposed to approx-imate unknown system states,based on which a adaptive output feedback controller is designed via Backstepping design method.By introducing a quartic Lyapunov function and using LaSalle-type theorem,it is shown that all signals in the closed-loop system are bounded almost surely and the solution is almost surely asymptotically stable.Finally,a simulation example is given to illustrate the effectiveness of the proposed results.4.The problem of noise-to-state stability(NSS)and globally asymptotic stability(GAS)is investigated for a class of nonlinear systems with random disturbances and impulses,where the random noises have finite second-order moments and the so-called random impulses mean that impulse ranges are driven by a sequence of random variables.First,some general conditions are given to guarantee the existence and uniqueness of solu-tions to random nonlinear impulsive systems.Next,when the continuous dynamics are stable but the impulses are destabilizing,the NSS and GAS of random nonlinear impul-sive systems are examined by the average impulsive interval approach.Then,when the continuous dynamics are unstable but the impulses are stabilizing,it is shown that the NSS and GAS can be retained by using the reverse average impulsive interval approach.Finally,the theoretical findings are substantiated with illustrative examples.5.The stability problem for switched nonlinear systems with random disturbances whose second-order moments are finite.First,some general conditions are given to guarantee the existence and uniqueness of solutions to random switched systems.Next,these re-sults are used to deduce the criteria of noise-to-state stability under probabilistic switch-ing signal.Then,the average dwell-time approach is adopted to study the noise-to-state stability and the global asymptotic stability of random switched systems.All the criteria on global existence and stability of solutions are developed by virtue of multiple Lya-punov functions.Finally,two numerical examples are given to demonstrate the validity of the theoretical results.6.This chapter aims to gain an insight into the Markovian switching random systems with stochastic processes whose second-order moments are finite.Compared with the exist-ing results,the existence and uniqueness of solutions to random systems with Marko-vian switching is not given as a priori information but guaranteed under some general conditions.The corresponding criteria on noise-to-state stability and boundedness are presented by employing the Lyapunov method.Finally,based on the derived results,a design procedure of state-feedback tracking control is proposed,which is illustrated through two examples.