Practically Predefined-Time Adaptive Fuzzy Tracking Control for Nonlinear Stochastic Systems

This article addresses the practically predefined-time adaptive fuzzy tracking control problem of strict-feedback nonlinear stochastic systems, where the system under consideration includes stochastic disturbances and uncertain parameters. First, in this study, practically predefined-time stochastic stabilization (PPSS) in the $p$ th moment sense is introduced, and a Lyapunov-type criterion for PPSS is proposed to assure the stabilization of the system considered. With these ideas, based on the backstepping design method, a semiglobally practically predefined-time adaptive fuzzy tracking control algorithm is proposed with a fuzzy system used to approximate the unknown part of the system. Moreover, the settling time of the system response can be arbitrarily adjusted in a mean-value sense, and such freedom can be used to improve the stochastic finite-/fixed-time control results. Finally, a practical example and a numerical example of a comparison are provided to validate the effectiveness of the proposed control strategy.