Research On Control Problems Of Stochastic Nonlinear Systems Based On Backstepping Methods

Nonlinear,time-delay and external stochastic disturbance are commonly encountered in real systems,and they always cause instability and oscillation.Hence,the study of stochastic nonlinear systems and time-delay systems has received much attention,especially,the finite-time stabilization now is the research focus.For several classes of stochastic nonlinear systems,the problems of controller design and stability analysis are investigated in this paper.The main contributions include:1.For a class of stochastic nonlinear time-delay systems with unknown output function,we find the maximal open sector of output function,by overcoming the difficulties of nonlinear terms arising from stochastic system,as long as output function belongs to any closed sector included in the maximal open sector,an output feedback controller can be designed to guarantee the closed-loop system globally asymptotically stable in probability.2.For a class of uncertain stochastic feedforward nonlinear systems with state and input de-lays,by introducing appropriate variable transformation and coordinate transformations,using homogeneous domination approach and stochastic Backstepping method,choosing appropriate Lyapunov-Krasovskii functional and regulative gain,and finding the maximal open sector of output function,we design an output feedback controller to guarantee the closed-loop system globally asymptotically stable in probability.3.For a class of stochastic high-order nonlinear systems with stochastic inverse dynamics,by characterizing unmeasured stochastic inverse dynamics with finite-time stochastic input-to-state stability(FT-SISS),borrowing from some ideas of Lyapunov function,sign function,FT-SISS methods and Backstepping method,and using stochastic finite-time stability theory,a new design and analysis method is given to guarantee global finite-time stability in probability of the closed-loop stochastic systems.4.For a class of stochastic low-order nonlinear systems with stochastic inverse dynamics,by choosing appropriate restrictive condition of nonlinear functions and constructing appropri-ate Lyapunov function,we design a finite-time stable state feedback controller for stochastic low-order nonlinear systems.5.For a class of stochastic nonlinear time-delay systems without imposing any restrictive condition on nonlinear function,by dynamic gain method,we construct a delay-independent,dynamic state feedback controller to make the closed systems globally asymptotically stable in probability.6.For a class of stochastic cascade nonlinear time-delay systems with stochastic inverse dynamics,by characterizing unmeasured stochastic inverse dynamics with SISS condition,without imposing any growth condition on time-delay system nonlinearities,a delay-independent,dynamic state feedback controller is constructed.It is shown that the equilibrium of the closed-loop system is globally asymptotically stable in probability.