Robust adaptive stabilizer of a class of time-varying plants using multiple controllers

Abstract

This paper presents an indirect adaptive control scheme for nominally stabilizable, non-necessarily inversely stable, first-order continuous-time systems with unmodeled dynamics. The control objective is the adaptive stabilization of the closed-loop system with a bounded tracking error between the system output and a reference signal given by a stable filter. The adaptive control scheme includes several estimation algorithms and a supervisor to select the appropriate estimator at certain time instants while keeping it in operation during at least a minimum residence or dwell time. Such selection is based on a criterion relative to the estimation errors obtained with each estimator. All estimators are of either least square or gradient type. The estimators include relative dead-zones for robustness purposes and parameter ‘a posteriori’ modifications to ensure the controllability of the estimated models of the plant. This is crucial to prove the stabilizability of the plant via adaptive pole-placement designs. The multi-estimation scheme renders the overall system highly nonlinear.