A Predictor-Based Model Reference Adaptive Controller for Time-Delay Systems

This paper presents novel modifications to a predictor-based model reference adaptive controller (PMRAC) to compensate for input delays in uncertain nonlinear systems. A delay-dependent stability condition, derived using a Lyapunov-Krasovskii functional, indicates that there exists a time delay margin, below which the asymptotic stability of the tracking and estimation errors as well as the input-to-state stability of the closed-loop system are guaranteed. Numerical experiments are carried out with comparisons to the original PMRAC and to a finite spectrum assignment scheme to validate the theoretical claims. The results also illustrate the effectiveness of the proposed delay compensation formulation and the asymptotic behaviors of the tracking and estimation errors.