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Zbl 1154.93427
Xie, Xue-Jun; Tian, Jie
Adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization. (English)
[J] Automatica 45, No. 1, 126-133 (2009). ISSN 0005-1098

Summary: This paper investigates the adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization. By using the parameter separation lemma in [{\it W. Lin} and {\it 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 2000:: *93D21 Adaptive and robust stabilization
93E15 Stochastic stability
93E03 General theory of stochastic systems
93E12 System identification (stochastic systems)

Keywords: high-order stochastic systems; nonlinear parameterization; adaptive state-feedback stabilization

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