Output-feedback control of stochastic nonlinear system with stochastic inverse dynamics

This paper considers a concrete stochastic nonlinear systems with stochastic unmeasurable inverse dynamic. Motivated by the concept of integral input-to-state stability (iISS) in deterministic systems and stochastic input-to-state stability (SISS) in stochastic systems, a concept of stochastic integral input-to-state stability (SiISS) using Lyapunov function is introduced. A constructive strategy is proposed to design a dynamic output-feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.