Study On Backstepping Control And Stabilization Of Stochastic Nonlinear Systems

Stochastic nonlinear systems have been widely used in many practical engineering model,such as mechanical systems and electric systems.Since many external noises(e.g.,stochastic disturbance and nonlinear perturbation)occur into systems,the stabilization problem of stochastic nonlinear systems has been one of hot topics in modern control theory.Recently,many system control methods have been proposed,such as backstepping method,neural network control,fuzzy control,etc.These methods have been applied into the controllers design of stochastic nonlinear systems.As a complete nonlinear control methodology,the backstepping method,which owns strong anti-interference ability,has been received extensive attention by researchers.In the dissertation,the feedback controller design problems for several classes of stochastic nonlinear systems are studied.By employing adding a power integrator,the concept of homogeneity,time-varying technique and adaptive control in the backstepping framework,we cope with many uncertains/unknowns(e.g.,high-order terms,unknown parameters,time variations and unmeasured states)during the control scheme.Moreover,based on stochastic stability theory,such as finite-time stability and globally asymptotic stability,we achieve the stabilization of the closed-loop systems by constructing appropriate Lyapunov functions.The main work of this thesis includes the following parts:1.The problem of finite-time state-feedback stabilization of a class of high-order stochastic nonlinear systems is studied.By virtue of the Ito formula,sign function and backstepping iteration,we design a continuous state-feedback controller to guarantee that the closed-loop system has a solution and the solution of the entire system is finite-time stable in probability.To proceed the backstepping procedure,a novel form of control parameters qi(i=1,...,n)is introduced into the control scheme.Finally,three simulations are presented to illustrate the effectiveness of the state-feedback controller.2.The problem of constructing C1 and smooth state-feedback controllers for a class of stochastic nonlinear systems in lower-triangular form is investigated.By using the backstepping method,the concept of homogeneity with monotone degrees(HWMD)and sign function,we design a C1 state-feedback controller step by step.By introducing a polynomial Lyapunov function with sign functions,we achieve that the solution to the closed-loop system is globally asymptotically stable in probability.In addition,a smooth state-feedback controller for a class of three-dimensional stochastic nonlinear systems is constructed by modifying the systems' homogeneities.Then,three simulation examples are given to show the effectiveness of the controllers.3.The output-feedback control of a class of non-autonomous stochastic feed-forward systems is considered.Since many unknowns occur into the systems,all the states of the systems are unmeasurable or unknown.It implies that these states are not available in the control scheme.To compensate the systems' states,a full-order K-filters is introduced into the backstepping design.By employing the sector region theory and time-varying technique,we design a time-varying output-feedback controller.Based on the improved LaSalle-type theorem,we prove the global regulation of the closed-loop system.In the end,an induction heater circuit system is presented to verify our control scheme.4.The problem of adaptive output-feedback control of nonlinearly parameterized stochastic nonholonomic systems is studied.Since unknown control coefficients and unknown nonlinear parameters occur into systems,we utilize an adaptive control method,together with a parameter separation technique,to construct an adaptive output-feedback controller to regulate the whole systems.During the design procedure,a new form of reduced-order K-filters is given to compensate the unmeasured states of the systems.A switching strategy is proposed explicitly in the control scheme.Finally,a bilinear model with stochastic disturbances is presented to demonstrate our theoretical results.