State-Feedback Stabilization for High-Order Stochastic Nonlinear Systems with Stochastic Inverse Dynamics

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, infin), 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.