ROBUST ADAPTIVE CONTROL WITH MULTIPLE ESTIMATION MODELS FOR STABILIZATION OF A CLASS OF NON‐INVERSELY STABLE TIME‐VARYING PLANTS

Abstract

ABSTRACTThis paper presents an indirect adaptive control scheme for nominally stabilizable non‐necessarily inversely stable continuous‐time systems with unmodelled dynamics. The control objective is the adaptive stabilization of the closed‐loop system with the achievement of 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 which selects the appropriate estimator at every certain time and keeping it operating for at least a minimum period of residence time. This selection is based on a performance criterion related to a measure of the estimation errors obtained with each estimator. In this way, the performance of the output signal is improved with regard to the performance achieved with a unique estimation algorithm. All the estimators are either of the least‐squares type or gradient type. However, any well‐posed estimation algorithm is potentially valid for application. These estimators include relative dead‐zones for robustness purposes and parameter ‘a posteriori’ modifications to ensure the controllability of the estimated models of the plant, which is crucial for proving the stabilizability of the plant via adaptive pole‐placement designs.