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Adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization. (English) Zbl 1154.93427
Summary: This paper investigates the adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization. By using the parameter separation lemma in [W. Lin and C. Qian, Adaptive control of nonlinearly parameterized systems: A nonsmooth feedback framework. IEEE Trans. Autom. Control 47, 757–774 (2002)] 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.
MSC:
93D21Adaptive or robust stabilization
93E15Stochastic stability
93E03General theory of stochastic systems
93E12System identification (stochastic systems)