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On periodic solutions of adaptive systems in the presence of periodic forcing terms. (English) Zbl 0712.93031
This paper studies solutions of adaptive feedback loops in the presence of unmodeled dynamics if the discrete-time linear plant. It assumes that the reference output is periodic with period K. The aim is to find K- periodic solutions of the adaptive system and study their stability. Sufficient conditions to have K-periodic solutions are derived. Also, the stability of these solutions is studied assuming that adaptation is slow. A wide class of direct adaptive controllers is used for checking the sufficient conditions for the existence of a periodic solution. It is proved that “almost always” the periodic solution exists, but no tools to study its stability, except in the exact modeling case, are available. The present study would be a first step toward a complete description of the behavior of an adaptive controller in feedback with a high-order linear plant.
Reviewer: P.Stoica

MSC:
93C40 Adaptive control/observation systems
93C05 Linear systems in control theory
93C55 Discrete-time control/observation systems
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