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Algebraic and Symbolic Computation Methods in Dynamical Systems pp 117–146Cite as

Thomas Decomposition and Nonlinear Control Systems

Part of the Advances in Delays and Dynamics book series (ADVSDD,volume 9)

Abstract

This paper applies the Thomas decomposition technique to nonlinear control systems, in particular to the study of the dependence of the system behavior on parameters. Thomas’ algorithm is a symbolic method which splits a given system of nonlinear partial differential equations into a finite family of so-called simple systems which are formally integrable and define a partition of the solution set of the original differential system. Different simple systems of a Thomas decomposition describe different structural behavior of the control system in general. The paper gives an introduction to the Thomas decomposition method and shows how notions such as invertibility, observability and flat outputs can be studied. A Maple implementation of Thomas’ algorithm is used to illustrate the techniques on explicit examples.

Keywords

  • Thomas decomposition
  • Differential elimination
  • Nonlinear control systems
  • Flatness
  • Observability
  • Invertibility
  • Parameters in nonlinear control system

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Acknowledgements

The first author was partially supported by Schwerpunkt SPP 1489 of the Deutsche Forschungsgemeinschaft. The authors would like to thank an anonymous referee for several useful remarks. They would also like to thank S. L. Rueda for pointing out reference [34].

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Ostwestfalen-Lippe University of Applied Sciences and Arts, Campusallee 12, 32657, Lemgo, Germany

    Markus Lange-Hegermann

  2. Centre for Mathematical Sciences, Plymouth University, 2-5 Kirkby Place, Drake Circus, Plymouth, PL4 8AA, UK

    Daniel Robertz

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  1. Markus Lange-Hegermann
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Correspondence to Daniel Robertz .

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Editors and Affiliations

  1. Inria Paris, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne University, Paris, France

    Dr. Alban Quadrat

  2. Lehrstuhl D fuer Mathematik, RWTH Aachen University, Aachen, Germany

    Prof. Dr. Eva Zerz

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Lange-Hegermann, M., Robertz, D. (2020). Thomas Decomposition and Nonlinear Control Systems. In: Quadrat, A., Zerz, E. (eds) Algebraic and Symbolic Computation Methods in Dynamical Systems. Advances in Delays and Dynamics, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-030-38356-5_4

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