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Control of Piecewise-Linear Hybrid Systems on Simplices and Rectangles

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Hybrid Systems: Computation and Control (HSCC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2034))

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Abstract

A necessary and sufficient condition for the reachability of a piecewise-linear hybrid system is formulated in terms of reachability of a finite-state discrete-event system and of a finite family of affine systems on a polyhedral set. As a subproblem, the reachability of an affine system on a polytope is considered, with the control objective of reaching a particular facet of the polytope. If the polytope is a simplex, necessary and sufficient conditions for the solvability of this problem by affine state feedback are described. If the polytope is a multi-dimensional rectangle, then a solution is obtained using continuous piecewise-affine state feedback.

Research is supported in part by the Project Verification of Hybrid Systems (VHS, Esprit Project 26270) of the European Commission.

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Author information

Authors and Affiliations

  1. CWI — Centrum voor Wiskunde en Informatica, P.O. Box 94079, 1090, GB Amsterdam, The Netherlands

    Luc C. G. J. M. Habets & Jan H. van Schuppen

  2. Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600, MB Eindhoven, The Netherlands

    Luc C. G. J. M. Habets

Authors
  1. Luc C. G. J. M. Habets
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  2. Jan H. van Schuppen
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Editor information

Editors and Affiliations

  1. Dipartimento di Ingegneria Elettrica, Universitá dell’Aquila, Poggio di Roio, 67040, L’Aquila, Italy

    Maria Domenica Di Benedetto

  2. University of California at Berkeley, Berkeley, CA, 94720

    Alberto Sangiovanni-Vincentelli

  3. PARADES, Via San Pantaleo, 66, 00186, Roma, Italy

    Alberto Sangiovanni-Vincentelli

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© 2001 Springer-Verlag Berlin Heidelberg

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Habets, L.C.G.J.M., van Schuppen, J.H. (2001). Control of Piecewise-Linear Hybrid Systems on Simplices and Rectangles. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A. (eds) Hybrid Systems: Computation and Control. HSCC 2001. Lecture Notes in Computer Science, vol 2034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45351-2_23

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  • DOI: https://doi.org/10.1007/3-540-45351-2_23

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  • Print ISBN: 978-3-540-41866-5

  • Online ISBN: 978-3-540-45351-2

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