IEEE Transactions on Automatic Control, Vol.66, No.3, 1306-1313, 2021
Adaptive Finite-Time Stabilization of Stochastic Nonlinear Systems Subject to Full-State Constraints and Input Saturation
In this article, the adaptive finite-time tracking control is studied for state constrained stochastic nonlinear systems with parametric uncertainties and input saturation. To this end, a definition of semiglobally finite-time stability in probability (SGFSP) is presented and a related stochastic Lyapunov theorem is established and proved. To alleviate the serious uncertainties and state constraints, the adaptive backstepping control and barrier Lyapunov function are combined in a unified framework. Then, by applying a function approximation method and the auxiliary system method to deal with input saturation respectively, two adaptive state-feedback controllers are constructed. Based on the proposed stochastic Lyapunov theorem, each constructed controller can guarantee the closed-loop system achieves SGFSP, the system states remain in the defined compact sets and the output tracks the reference signal very well. Finally, a stochastic single-link robot system is established and used to demonstrate the effectiveness of the proposed schemes.
Keywords:Nonlinear systems;Stochastic processes;Adaptive systems;Uncertainty;Stability analysis;Backstepping;Lyapunov methods;Adaptive finite-time control;barrier Lyapunov function (BLF);full-state constraints;input saturation;semi-globally finite-time stability in probability (SGFSP);stochastic nonlinear systems