PERSISTENT IDENTIFICATION AND ADAPTATION - STABILIZATION OF SLOWLY VARYING SYSTEMS IN H-INFINITY

In this paper, the problem of persistent identification and adaptive s tabilization of time-varying systems is studied within the framework o f deterministic worst case identification and slow H-infinity adaptati on. The plants under consideration are unstable and time-varying and c annot be stabilized by a fixed robust controller. Starting from an ini tial well-designed operating point, the controller must persistently a dapt to the time-varying plant to maintain uniform stability over all future time. A key property which guarantees uniform stability is that the identification-adaptation iteration satisfies a certain invarianc e principle. We demonstrate that the adaptive design using periodic ex ternal inputs, least squares identification, and slow H-infinity adapt ation possesses such an invariance property, leading to a successful a daptive stabilization methodology. Generic natures of our findings are discussed.