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The Extended Linear Complementarity Problem and the Modeling and Analysis of Hybrid Systems

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Hybrid Systems V (HS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1567))

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Abstract

First we give a short description of the Extended Linear Complementarity Problem (ELCP), which is a mathematical programming problem. We briefly discuss how this problem can be used in the analysis of discrete event systems and continuous variable systems. Next we show that the ELCP can also be used to model and to analyze hybrid systems. More specifically, we consider a traffic-light-controlled intersection, which can be considered as a hybrid system. We construct a model that describes the evolution of the queue lengths in the various lanes (as continuous variables) as a function of time and we show that this leads to an ELCP. Furthermore, it can be shown that some problems in the analysis of another class of hybrid systems, the “complementary-slackness systems”, also lead to an ELCP.

Senior research assistant with the F.W.O. (Fund for Scientific Research-Flanders).

Research associate with the F.W.O.

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Authors and Affiliations

  1. ESAT-SISTA, K.U.Leuven, Kardinaal Mercierlaan 94, B-3001, Leuven, Belgium

    Bart De Moor

Authors
  1. Bart De Schutter
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  2. Bart De Moor
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    Panos Antsaklis  & Michael Lemmon  & 

  2. Hynomics Corporation, 10632 NE 37th Circle, Building 23, Kirkland, WA, 98033, USA

    Wolf Kohn

  3. Department of Mathematics, Cornell University, 217, White Hall, Ithaca, NY, 14853, USA

    Anil Nerode

  4. Electronic Research Laboratory, University of California at Berkeley, 253 Cory Hall, Berkeley, CA, 94720, USA

    Shankar Sastry

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© 1999 Springer-Verlag Berlin Heidelberg

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De Schutter, B., De Moor, B. (1999). The Extended Linear Complementarity Problem and the Modeling and Analysis of Hybrid Systems. In: Antsaklis, P., Lemmon, M., Kohn, W., Nerode, A., Sastry, S. (eds) Hybrid Systems V. HS 1997. Lecture Notes in Computer Science, vol 1567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49163-5_4

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  • DOI: https://doi.org/10.1007/3-540-49163-5_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65643-2

  • Online ISBN: 978-3-540-49163-7

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