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Hybrid Kernels and Capture Basins for Impulse Constrained Systems

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Book cover Hybrid Systems: Computation and Control (HSCC 2002)

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Abstract

We investigate, for constrained controlled systems with impulse, the subset of initial positions contained in a set K from which starts at least one run viable in K - the hybrid viability kernel - eventually until it reaches a given closed target in finite time - the hybrid capture basin. We define a constructive algorithm which approximates this set. The knowledge of this set is essential for control problem since it provides viable hybrid feed-backs and viable runs. We apply this method for approximatingt he Minimal Time-to-reach Function in the presence of both constraints and impulses. Two examples are presented, the first deals with a dynamical system revealingthe complexity of the structure of hybrid kernels, the second deals with a Minimal Time problem with impulses.

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Author information

Authors and Affiliations

  1. Centre of Recherche Viabilité, Jeux, Contrôle, Université Paris IX, Dauphine

    Patrick Saint-Pierre

Authors
  1. Patrick Saint-Pierre
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Editor information

Editors and Affiliations

  1. Department of Aeronautics and Astronautics, Stanford University, 250 Durand Building MC4035, 94305-4035, Stanford, CA, USA

    Claire J. Tomlin

  2. Department of Computer Science, University of British Columbia, 201-2366 Main Mall, V6T1Z4, Vancouver BC, Canada

    Mark R. Greenstreet

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Saint-Pierre, P. (2002). Hybrid Kernels and Capture Basins for Impulse Constrained Systems. In: Tomlin, C.J., Greenstreet, M.R. (eds) Hybrid Systems: Computation and Control. HSCC 2002. Lecture Notes in Computer Science, vol 2289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45873-5_30

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  • DOI: https://doi.org/10.1007/3-540-45873-5_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43321-7

  • Online ISBN: 978-3-540-45873-9

  • eBook Packages: Springer Book Archive

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