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Invariant tracking

Published online by Cambridge University Press:  15 February 2004

Philippe Martin ,
Pierre Rouchon  and
Joachim Rudolph
Philippe Martin
Affiliation:
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.
Pierre Rouchon
Affiliation:
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.
Joachim Rudolph
Affiliation:
Institut fur Regelungs- und Steuerungstheorie, Technische Universität Dresden, Mommsenstr. 13, 01062 Dresden, Germany; rudolph@erss11.et.tu-dresden.de.
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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.

Keywords

Symmetriesinvariantsnonlinear controloutput trackingdecoupling.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 10 , Issue 1 , January 2004 , pp. 1 - 13
Copyright
© EDP Sciences, SMAI, 2004

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