Fixed-Time Adaptive Fuzzy Control for Nonstrict Feedback High-Order Stochastic Nonlinear Systems With State Constraints

This article considers the issue of adaptive fixed-time tracking control for a class of stochastic high-order nonlinear systems (HONSs) with full state constraints. Unlike the existing results, a Barrier Lyapunov function (BLF) with fractional form is employed to deal with asymmetric full-state constraints. Fuzzy logic systems are employed to resolve stochastic disturbances and unknown nonlinearities. Based on adding a power integrator technique and backstepping method, an adaptive fixed-time fuzzy state feedback controller is proposed to ensure that all signals are bounded and all states are always within the constrained interval. The nonlinear system is fixed-time bounded in probability by the fixed-time Lyapunov stability theory. Without altering the controller structure, the BLF can be used in unconstrained high-order systems. Two simulation experiments including a spring-mass damper system prove the effectiveness of the designed control strategy.