Continuous‐Time Model Reference Adaptive Control

Abstract

This chapter deals with continuous-time model reference adaptive control using output feedback for output tracking. The key components of model reference adaptive control theory - a priori plant knowledge, controller structure, plant-model matching, adaptive laws, stability, robustness, and robust adaptation - are addressed in a comprehensive formation and, in particular, stability and robustness analysis is given in a simplified framework. The plant-model matching equation for a standard model reference controller structure is studied in a tutorial formula. Design and analysis of model reference adaptive control schemes are given for plants with relative degree 1 or larger, using a Lyapunov or gradient method based on a standard quadratic or nonquadratic cost function. Robust adaptive control is formulated and solved in a compact framework. Assumptions on plant unmodeled dynamics are clarified, and robust adaptive laws are analyzed. Closed-loop signal boundedness and mean tracking error properties are proved. To develop adaptive control schemes without using the sign of the high frequency gain of the controlled plant, a modified controller parametrization leads to a framework of adaptive control using a Nussbaum gain for stable parameter adaptation and closed-loop stability and asymptotic output tracking.