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Flatness of nonlinear control systems and exterior differential systems

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Nonlinear control in the year 2000 volume 2

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 259))

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Abstract

Necessary and sufficient conditions for k-flatness are given. We construct an exterior differential system (I, Θ) and show that (local) k-flatness is equivalent to the existence of (local) integral manifolds of (I, Θ), which is in turn equivalent to the existence of a solution of a partial differential equation. As a consequence, the k-flatness of a nonlinear system can be checked with convenient applications of Cartan-Kähler and Cartan-Kuranishi theorems. Some academic examples are presented to illustrate the result.

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Authors and Affiliations

  1. Escola Politécnica da USP — PTC, 05508-900, São Paulo — SP, Brazil

    Paulo Sérgio Pereira da Silva

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  1. Paulo Sérgio Pereira da Silva
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Alberto Isidori Françoise Lamnabhi-Lagarrigue Witold Respondek

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© 2001 Springer-Verlag London Limited

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da Silva, P.S.P. (2001). Flatness of nonlinear control systems and exterior differential systems. In: Isidori, A., Lamnabhi-Lagarrigue, F., Respondek, W. (eds) Nonlinear control in the year 2000 volume 2. Lecture Notes in Control and Information Sciences, vol 259. Springer, London. https://doi.org/10.1007/BFb0110303

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  • DOI: https://doi.org/10.1007/BFb0110303

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-364-5

  • Online ISBN: 978-1-84628-569-1

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