Adaptive fuzzy fixed time control for pure-feedback stochastic nonlinear systems with full state constraints

In this paper, an adaptive fuzzy fixed time control scheme is developed for stochastic pure-feedback nonlinear systems with full state constraints. The mean value theorem is exploited to deal with the problem of nonaffine appearance in the systems and transform the structure of pure-feedback to the structure of strict-feedback. The barrier Lyapunov functions are constructed to guarantee that all states in the systems maintain within the prescribed constraints and the fuzzy logic systems are employed to approximate unknown nonlinear functions at each step. Then, an adaptive fuzzy fixed time controller is constructed by utilizing backstepping technique, which guarantees that all the signals in the considered systems are semiglobally uniform ultimately bounded in a fixed time. Finally, the validity of the proposed fixed time control scheme is verified via a simulation example.