A Simplified Adaptive Fixed Time Control of Pure-Feedback Stochastic Nonlinear Systems Subject to Full State Constraints

Abstract

In this paper, a novel fixed time adaptive fuzzy control scheme for pure-feedback stochastic nonlinear systems with full state constraints is proposed based on dynamic surface control (DSC) technique and barrier Lyapunov functions (BLFs) method. Firstly, the mean value theorem is utilized to transform the pure-feedback structure of the considered systems into strict-feedback ones, which make it possible for the utilization of backstepping method to design the controller. Then, DSC technique is used to reduce the computational complexity problem caused by backstepping method. Fuzzy logic systems are exploited to approximate the unknown nonlinear functions. Moreover, combine BLFs method with fixed time stability theorem, the fixed time adaptive fuzzy controller is constructed, which guarantees that all states do not violate the prescribed constraints and all signals are semi-globally uniform ultimately bounded. Finally, a simulation example is given to verify the effectiveness of the studied control.