Adaptive Fuzzy Control for High-Order Nonlinear Time-Delay Systems With Full-State Constraints and Input Saturation

Abstract

This paper investigates adaptive fuzzy tracking control for high-order nonlinear time-delay systems with full-state constraints and input saturation. By adopting fuzzy approximation technique, frequently used growth assumptions imposed on unknown system nonlinearities are removed. High-order barrier Lyapunov functions are employed to prevent the transgression of full-state constraints. The auxiliary subsystem and the Nussbaum gain technique are utilized to analyze the effect of input saturation. Appropriate Lyapunov-Krasovskii functionals are constructed to compensate the adverse effect caused by the unknown time-delay. Novel feasibility conditions are formulated as sufficient conditions for the existence of proposed control. It is rigorously proved that all the closed-loop signals are bounded in the semi-global sense, error signals converge to small bounded compact sets, full-state constraints, and input saturation are not violated, and the arguments of unknown nonlinearities are constrained within a compact set, on which fuzzy approximation is valid. Eventually, the theoretical result is confirmed by two simulation examples.