Fast finite-time adaptive tracking control for non-strict feedback stochastic nonlinear systems with full state constraints

This article focuses on the fast finite-time adaptive tracking control for non-strict feedback stochastic nonlinear systems. Random disturbances with constraints have rarely been considered in previous studies of fast finite-time stabilization problems. The corresponding extension of the adaptive fast finite-time stabilization mechanism to stochastic nonlinear systems with full-state constraints is one of the innovations of this article. First, neural networks and barrier Lyapunov functions are utilized to handle the problems arising from the unknown nonlinear terms and the state constraints, respectively. Second, an adaptive fast finite-time tracking control scheme for stochastic systems is designed based on the backstepping technique and a fast finite-time control strategy, which allows all signals of the closed-loop system to be bounded. Meanwhile, the designed controller guarantees a fast convergence of the tracking error to a small neighborhood of the origin under full-state constraints. Finally, two examples are given to illustrate the feasibility of the proposed method.