Identification and adaptive stabilization of slowly varying systems: an H∞ approach

In this paper, the problems of identification and adaptation of slowly time-varying systems are investigated, using the idea of identification and slow adaptation in an H^∞ framework. We consider in this paper the stabilization problem of a class of systems with time-varying H^∞-type unstructured uncertainties. It is shown that when a priori uncertainty sets are large, there exists no nonadaptive robust control to stabilize them. As a result, persistent adaptation based on a posteriori information is inevitable. To gain a better understanding of the ability of an adaptive system to adapt with a time-varying environment, we focus on the behavior of the adaptive system after arriving at its initial a posteriori uncertainty set. A design procedure is developed which employs the ideas of persistent dithering, identification, and slow H ^∞ adaptation