Finite-Time Control And Analysis For Stochastic Nonlinear Systems

In resent years, finite-time controller design for nonlinear systems has been a hot research topic in the control field. Besides faster convergence, finite-time stable control systems have better robustness and dis-turbance rejection properties than asymptotically stable control systems. Since stochastic models have a wide application, the controller design for stochastic nonlinear systems has attracted much attention. It is rather difficult to design the controller due to the influence of nonlinear terms and stochastic factors in stochastic nonlinear systems. When we consider the finite-time controller design for stochastic nonlinear systems, it is hard to analyse the existence of a strong solution due to lack of the local Lipschitz condition.We consider finite-time control for the weak solution. Under the framework of the weak solution, two finite-time stability theorems are given, and global finite-time stabilization by state feedback is investigated for two classes of stochastic nonlinear systems. The main work includes:1). For stochastic nonlinear systems, we introduce the definition of a weak solution and the theorem about the existence of a local weak solution. The definition of global finite-time stability in probability is given when a weak solution exists globally. When drift and diffusion terms of stochastic nonlinear systems are continuous, two theorems are given to prove that the equilibrium of stochastic nonlinear systems is globally finite-time stable in probability.2). Under the assumption that stochastic inverse dynamics are stochastic input-to-state stable, a finite-time controller via state feedback is constructively designed for a class of stochastic nonlinear systems with stochastic inverse dynamics by the methods of backstepping and changing supply functions. The closed-loop system is proved to be globally finite-time stable in probability. A simulation example is given to illustrate the efficiency of the proposed design method.3). For a class of continuous but non-smooth stochastic nonlinear systems, state-feedback controllers are constructively designed for global finite-time stabilization. A simulation example is given to illustrate the efficiency of the proposed design procedure.