Adaptive predefined-time tracking control for stochastic nonlinear systems subject to asymmetric output constraints

This paper investigates the predefined-time tracking control problem for a type of strict-feedback stochastic nonlinear systems, in which the output variable is required to be constrained within an asymmetric interval and the nonlinearities are unknown. First, an improved practical predefined-time stability (PPTS) Lyapunov criterion for stochastic nonlinear systems is presented. Secondly, an asymmetric integral barrier Lyapunov function is constructed to handle the output constraint issue. On this basis, an adaptive predefined-time adaptive fuzzy tracking control algorithm is developed via the backstepping framework, where fuzzy logic systems (FLSs) are utilized to approximate unknown system dynamics. Through rigorous mathematical analysis and numerical simulations, it can be concluded that the proposed control scheme can not only drive all system variables to converge to steady states within a prescribed time in probability, but also make the output track the desired signal without violating the output constraint.