Adaptive Fuzzy Inverse Optimal Output Regulation for a Class of Nonlinear Time-Delay Systems

Abstract

This paper aims to solve the adaptive fuzzy inverse optimal output regulation problem for a class of uncertain nonlinear systems with the exosystem. Both unknown nonlinear functions and time-delay are considered here. The output regulation problem is first converted into a stabilization problem by employing the internal model principle. Then, fuzzy logic systems (FLSs) are employed to approximate unknown nonlinear functions. A new cost functional related to the internal model and time-delay is established. An auxiliary system connected to time-delay is constructed, and a new fuzzy state observer based on the auxiliary system is designed to estimate the unmeasured states. Further, by utilizing the adaptive backstepping control technique, the inverse optimal control method, and the Lyapunov–Krasovskii functional, a novel adaptive fuzzy inverse optimal output feedback controller and adaptive law are presented. It is also proved that all signals of the closed-loop system are globally uniformly ultimately bounded (UUB); the proposed controller can achieve inverse optimization by minimizing the cost functional. Finally, a simulation example is provided to prove the effectiveness of the method in this paper.