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Invariant tracking and stabilization: problem formulation and examples

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Stability and Stabilization of Nonlinear Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 246))

Abstract

The problems of invariant tracking and invariant stabilization are considered: Design a state feedback for tracking or stabilization, respectively, such that the closed-loop dynamics is invariant under the action of a given group. Errors are then defined as invariants of the group under consideration. The approach is illustrated on two classical examples: the nonholonomic car and a continuous stirred chemical reactor. In both cases the differential flatness of the models allows for a systematic design of feedback laws for invariant tracking. The feedback synthesis is simplified by using implicit system descriptions

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Author information

Authors and Affiliations

  1. Centre Automatique et Systèemes, École des Mines de Paris, 60, bd. Saint-Michel, 75272, Paris Cedex 06, France

    Pierre Rouchon

  2. Institut für Regelungs- und Steuerungstheorie, TU Dresden, Mommsenstr. 13, 01062, Dresden, Germany

    Joachim Rudolph

Authors
  1. Pierre Rouchon
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  2. Joachim Rudolph
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Editor information

Editors and Affiliations

  1. Dept. of Systems Dynamics, Universiteit Gent, Technologiepark-Zwijnaarde 9, 9052, Gent, Belgium

    Dirk Aeyels (Professor) (Professor)

  2. Laboratoire des Signaux et Systèmes, CNRS, SUPELEC, 91192, Gif-sur-Yvette, France

    Françoise Lamnabhi-Lagarrigue (Docteur d’état) (Docteur d’état)

  3. Dept. of Applied Mathematics, University of Twente, PO Box 217, 7500, Enschede, The Netherlands

    Arjan van der Schaft (Professor) (Professor)

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© 1999 Springer-Verlag London Limited

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Rouchon, P., Rudolph, J. (1999). Invariant tracking and stabilization: problem formulation and examples. In: Aeyels, D., Lamnabhi-Lagarrigue, F., van der Schaft, A. (eds) Stability and Stabilization of Nonlinear Systems. Lecture Notes in Control and Information Sciences, vol 246. Springer, London. https://doi.org/10.1007/1-84628-577-1_14

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  • DOI: https://doi.org/10.1007/1-84628-577-1_14

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-638-7

  • Online ISBN: 978-1-84628-577-6

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