Adaptive fuzzy fixed-time control for a class of strict-feedback stochastic nonlinear systems

This paper studies fixed-time tracking problems for stochastic nonlinear systems in strict-feedback form. Different from previous results, the practical fixed-time bounded theorem for stochastic nonlinear systems is given. The unknown functions of the stochastic nonlinear systems are approximated by the Fuzzy logic system (FLS) which has a universal approximation. Then by using a back-stepping method, a novel adaptive fuzzy fixed-time controller is designed for stochastic nonlinear systems based on the fixed-time bounded theorem. The states of the stochastic nonlinear systems are guaranteed to converge into an equilibrium point contained compact set semi-globally in fixed-time by the designed controller. Finally, a numerical example and a vehicle tracking model example are provided to illustrate the proposed strategy.