Adaptive fixed-time neural control of nonlinear time-varying state-constrained systems

In this paper, an adaptive fixed-time neural control scheme is proposed for a class of nonlinear uncertain systems with full-state constraints. A novel asymmetric hyperbolic barrier Lyapunov function (AHBLF) is first constructed to handle time-varying constraints of all the system states. EspecialLy, the AHBLF can not only be applied to unconstrained, symmetric-constrained and asymmetric-constrained systems simultaneously, but also the fixed time control can be realized by incorporating the AHBLF into each step of the backstepping method to design controller. The adaptive controller is presented to guarantee that the tracking errors converge into the neighborhood around the equilibrium point in a fixed time and all the system states can be restricted within the predefined time-varying boundaries. With the proposed control scheme, the singularity problem is avoided without constructing multiple piecewise functions, and no prior knowledge on the bound of gain functions is required in the controller design. Comparative simulations illustrate the effectiveness of the proposed control scheme.