Adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization

This paper investigates the adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization. By using the parameter separation lemma in [Lin, W., & Qian, C. (2002a). Adaptive control of nonlinearly parameterized systems: A nonsmooth feedback framework. IEEE Transactions on Automatic Control, 47, 757-774.] and some flexible algebraic techniques, and choosing an appropriate Lyapunov function, a smooth adaptive state-feedback controller is designed, which guarantees that the closed-loop system has an almost surely unique solution for any initial state, the equilibrium of interest is globally stable in probability, and the state can be regulated to the origin almost surely.