On periodic solutions of adaptive systems in the presence of periodic forcing terms |
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Authors: | J -B Pomet J -M Coron L Praly |
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Affiliation: | (1) Ecole des Mines, C.A.I. Section d’Automatique, 35 rue Saint Honoré, 77305 Fontainebleau Cédex, France |
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Abstract: | We consider a discrete-time system consisting of a linear plant and a periodically forced feedback controller whose parameters
are slowly adapted. Using degree theory, we give sufficient conditions for the existence of periodic solutions. Using linearization
methods, we give sufficient conditions for their (in)stability provided the adaptation is slow enough. We then study when
the degree theoretic conditions for the existence are satisfied byd-steps-ahead adaptive controllers in the presence of unmodeled dynamics and a persistently exciting periodic reference output. |
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Keywords: | Adaptive control Unmodeled dynamics Averaging analysis Periodic solutions Degree theory |
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