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State-feedback stabilization for high-order stochastic nonlinear systems with stochastic inverse dynamics. (English) Zbl 1127.93354
Summary: For a class of high-order stochastic nonlinear systems with stochastic inverse dynamics which are neither necessarily feedback linearizable nor affine in the control input, this paper investigates the problem of state-feedback stabilization for the first time. Under some weaker assumptions, a smooth state-feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on $$[0, \infty)$$, the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, and the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme.

##### MSC:
 93D15 Stabilization of systems by feedback 93E03 Stochastic systems in control theory (general) 93C10 Nonlinear systems in control theory
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