Adaptive Fixed-Time Fuzzy Control for Uncertain Nonlinear Systems with Asymmetric Time-Varying Full-State Constraints

In this paper, the adaptive fixed-time control problem is investigated for a class of uncertain nonlinear systems with asymmetric time-varying full-state constraints. A nonlinear state-constrained function (NSCF) is constructed to prevent the asymmetric time-varying full-state constraints from being violated. Different from the conventional used full-state constraints method (such as the barrier Lyapunov function (BLF) approach), the asymmetric and symmetric full-state constraints problem can be solved without switching controller structure and no additional assumption about virtual control is required to be satisfied by the NSCF approach. To overcome the “explosion of complexity” problem of the traditional backstepping method, the fixed-time command filters (FTCFs) are used to propose the control strategy. Furthermore, error compensation mechanisms are designed to remove the filtering errors induced by utilizing the FTCFs. Under the backstepping control framework, an adaptive fixed-time control strategy is designed to ensure that all signals in the closed-loop system and tracking error are bounded within fixed-time, and all states are guaranteed to maintain in the predefined regions. Finally, a simulation example is given to illustrate the effectiveness of the proposed control scheme.