On the Robustness of Discrete-Time Indirect Adaptive (Linear) Controllers

Remarkable research activity has been devoted to the design of certainty equivalence based adaptive controllers which perform well in those ubiquitous non-idealities as bounded disturbances, time varying parameters and some classes of unmodeled dynamics. The long-standing issue is the estimated model admissibility condition; i.e. the underlying linear control law should stabilize the estimated model. The motivation of this paper is twofold. The first one, which is a comprehensive synthesis in nature, is to propose a general framework for robustly designing the adaptive linear controllers, irrespective of the underlying control law, bearing in mind the available theoretical and practical results. The final motivation is to provide a new solution to the problem of the estimated model admissibility using an ad-hoc modification of the control law. Such a modification consists in adding a feedback impulse-exciting signal, while freezing the controller parameters, whenever the estimated model admissibility is lost.