Adaptive Fuzzy Asymptotic Tracking Control of State-Constrained High-Order Nonlinear Time-Delay Systems and Its Applications

This article discusses the adaptive fuzzy asymptotic tracking control for high-order nonlinear time-delay systems with full-state constraints. Fuzzy-logic systems and a separation principle are utilized to relax growth assumptions imposed on unknown nonlinearities. The adverse effect caused by unknown time delays is eliminated by choosing appropriate Lyapunov-Krasovskii functionals. By integrating nonlinear-transformed functions with a key coordinate transformation into the control design and constructing a specific compact set on the initial values of system states, the desired trajectory and parameter estimates, it is rigorously proved that all closed-loop signals are semiglobally bounded, the fuzzy approximation is valid, the full-state constraints are not violated without feasibility conditions on virtual controllers, and asymptotic tracking is achieved. The effectiveness and advantages of this control scheme are confirmed by two examples including a single-link robotic system.