Fixed-Time Neural Adaptive Control for Nonlinear Asymmetric Constrained Systems Subject to Time-Varying Input Delay

The present research addresses the issue of fixed-time (FxT) command filtered adaptive tracking control for a class of nonlinear system subject to time-varying input delay and error/state constraints. First, based on the existing FxT control theory, we present two new FxT stability lemmas, affording less conservative and more exact upper-bound estimates (UBEs) for the settling time. Second, the asymmetric constrained systems are reconstructed into novel systems devoid of constraints by introducing nonlinear transformation functions (NTFs), which remove the feasibility conditions related to the virtual controllers while satisfying the error and state constraints. Then, a novel FxT auxiliary system is established to effectively handle the input delay that is allowed to be unknown. By employing the FxT stability criterion and Lyapunov–Krasovskii functional approach, it is proved that the controlled systems are practically fixed-time stable (PFxTS) and do not violate their error/state constraints. Additionally, without the need for modifying the control framework, the control algorithm capably addresses the control issue uniformly for both constrained and unconstrained systems. In the end, a simulation example is given to check the validity of the main results.