CONTROLLABILITY AND PRACTICAL STABILIZATION OF NONLINEAR ITO-TYPE STOCHASTIC CONTROLLED SYSTEMS

摘要

In this paper, the concept of practical stability is investigated for a class of controlled stochastic systems of the Ito-Doob type. By using vector Lyapunov-like functions and comparison principle, sufficient conditions are established for various types of practical stability criteria in the p-th mean and in probability. This comparison principle allows one to determine the practical stability criteria of a nonlinear stochastic system by testing the practical stability of the corresponding auxiliary deterministic system with random initial condition. Finally, for the stochastic systems we discuss the controllability and study the optimal practical stabilization of controlled stochastic systems via the well known Hamilton-Jacobi-Bellman equation.