Adaptive state-feedback control for low-order stochastic nonlinear systems with an output constraint and SiISS inverse dynamics

This paper focuses on state-feedback adaptive control for stochastic low-order nonlinear systems with an output constraint and stochastic integral input-to-state stability (SiISS) inverse dynamics. The system with an output constraint was transformed straightforwardly into the equivalent system without a constraint using important coordinate transformations. SiISS was used to characterize unmeasured stochastic inverse dynamics. By introducing Lyapunov functions and using the stochastic systems stability theorem, we constructed a new adaptive state-feedback controller that assures the closed-loop system's trivial solution is stable in probability while fulfilling the requirements of the output constraint and all closed-loop signals are likely to be almost surely bounded. The validity of the control scheme presented in this paper was demonstrated by using simulation outcomes.