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Issue ESAIM: COCV
Volume 10, Number 1, January 2004
Page(s) 1 - 13
DOI 10.1051/cocv:2003037

ESAIM: COCV, January 2004, Vol. 10, pp. 1-13
DOI: 10.1051/cocv:2003037

Invariant tracking

Philippe Martin1, Pierre Rouchon1 and Joachim Rudolph2

1  Centre Automatique et Systèmes, École des Mines de Paris, 60 boulevard Saint-Michel, 75272 Paris Cedex 06, France; philippe.martin@ensmp.fr., pierre.rouchon@ensmp.fr.
2  Institut fur Regelungs- und Steuerungstheorie, Technische Universität Dresden, Mommsenstr. 13, 01062 Dresden, Germany; rudolph@erss11.et.tu-dresden.de.


(Received December 19, 2002. Revised April 2, 2003.)

Abstract
The problem of invariant output tracking is considered: given a control system admitting a symmetry group  G, design a feedback such that the closed-loop system tracks a desired output reference and is invariant under the action of  G. Invariant output errors are defined as a set of scalar invariants of  G; they are calculated with the Cartan moving frame method. It is shown that standard tracking methods based on input-output linearization can be applied to these invariant errors to yield the required "symmetry-preserving" feedback.


Mathematics Subject Classification. 53A55, 93C10, 93D25, 70Q05.

Key words: Symmetries, invariants, nonlinear control, output tracking, decoupling.


© EDP Sciences, SMAI 2004


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