Adaptive control of stochastic high-order nonlinearly parameterized systems with SiISS inverse dynamics

This paper focuses on the problem of adaptive state-feedback control for a class of stochastic high-order nonlinearly parameterized systems with stochastic integral input-to-state stable (SiISS) inverse dynamics. By employing the parameter separation principle and the tool of adding a power integrator, a one-dimensional adaptive state-feedback controller is constructed. On the basis of stochastic LaSalle theorem and SiISS small-gain type conditions, the proposed adaptive controller can guarantee that all signals of the closed-loop system are bounded almost surely and the stochastic closed-loop system is globally stable in probability. In addition, the aforementioned control scheme is generalized to some kinds of stochastic nonlinear systems with SiISS inverse dynamics, and some new control results are obtained. Two simulation examples are provided to verify the effectiveness of the adaptive controller.