Finite-time adaptive fuzzy control for strict feedback systems with asymmetric state constraints and prescribed performance

In practical systems, it is crucial to achieve the prescribed performance under system constraints. A novel finite-time adaptive fuzzy control strategy is proposed for strict feedback nonlinear systems subject to Asymmetric Time-Varying State Constraints (ATSCs) and Predefined Performance Indices (PPI). The proposed method employs an asymmetric barrier Lyapunov function to guarantee that the system states remain within the ATSCs while simultaneously ensuring that the output tracking error remains within the PPI defined by the finite-time performance function (FTPF). Furthermore, the strategy incorporates a disturbance observer, a fuzzy state observer, and the Dynamic Surface Control (DSC), thereby enhancing the practical applicability and robustness of the control design. The semi-global practical finite-time stability (SPFS) of the closed-loop system is rigorously established using Lyapunov-based analysis. The study of a one-link manipulator has verified the theoretical results and demonstrated the effectiveness and feasibility of the proposed control method.