Stability Controller Design For Two Classes Of Stochastic Nonlinear Systems

The controller design and stability analysis problems for stochastic nonlinearsystems are hot topics in recent years. This dissertation focuses on stability controllerdesign for two classes of stochastic systems. By using the method of integratorbackstepping, homogeneous system theory and some important inequalities, stabilizingstate-feedback controllers are designed respectively. In addition, by using stochasticanalysis tools and stability theorem for stochastic nonlinear systems, the performaceanalysis is given for closed-loop system. Numerical simulations examples illustrate theeffectiveness of the proposed approaches. The dissertation mainly inludes the followingtwo parts:Firstly, the state-feedback control problem is studied for a class of upper-triangularstochastic systems. By using the integrator backstepping design method, state-feedbackcontroller is designed for nominal system in the first step. Then, by using stochasticlow-gain homogeneous domination design method, the gains of the controller arecompared and chosen, and the smooth state-feedback controller is designed to solve thestate-feedback control problem for the original system. The controller can ensure thatthe closed-loop system has an almost surely unique solution on [0,∞)and theequilibrium at the origin of the closed-loop system is globally asymptotically stable inprobability. For a meaningful function, the inverse optimal controller is designed tosolve the problem of inverse optimal stabilization in probability for the investigatedsystem. Finally, a numerical example is provided to demonstrate the effectiveness ofthe proposed control scheme.Secondly, the adaptive state-feedback stabilization problem is considered for a classof high-order stochastic systems with time-varying control coefficients and moregeneral drift and diffusion terms. By using the parameter separation technique andhigh-gain homogeneous domination method, the power order restriction required in thetraditional results is completely cancelled, and the adaptive state-feedback controller isconstructed to ensure that the equilibrium at the origin of the closed-loop system isglobally asymptotically and the states can be regulated to the origin almost surely.The efficiency of control scheme is demonstrated by a numerical example.Finally, the research of the dissertation are summarized and future research topicsare pointed out.