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International Workshop on Hybrid Systems: Computation and Control

HSCC 2004: Hybrid Systems: Computation and Control pp 32–47Cite as

Abstraction by Projection and Application to Multi-affine Systems

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2993))

Abstract

In this paper we present an abstraction method for nonlinear continuous systems. The main idea of our method is to project out some continuous variables, say z, and treat them in the dynamics of the remaining variables x as uncertain input. Therefore, the dynamics of x is then described by a differential inclusion. In addition, in order to avoid excessively conservative abstractions, the domains of the projected variables are divided into smaller regions corresponding to different differential inclusions. The final result of our abstraction procedure is a hybrid system of lower dimension with some important properties that guarantee convergence results. The applicability of this abstraction approach depends on the ability to deal with differential inclusions. We then focus on uncertain bilinear systems, a simple yet useful class of nonlinear differential inclusions, and develop a reachability technique using optimal control. The combination of the abstraction method and the reachability analysis technique for bilinear systems allows to treat multi-affine systems, which is illustrated with a biological system.

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Author information

Authors and Affiliations

  1. LIAFA, Université Paris 7, 2 place Jussieu, Case 7014, 75251, Paris 5, France

    Eugene Asarin

  2. VERIMAG, Centre Equation, 2 av de Vignate, 38610, Gières, France

    Thao Dang

Authors
  1. Eugene Asarin
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  2. Thao Dang
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Editor information

Editors and Affiliations

  1. University of Pennsylvania,  

    Rajeev Alur

  2. School of Engineering and Applied Science, University of Pennsylvania,  

    George J. Pappas

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Asarin, E., Dang, T. (2004). Abstraction by Projection and Application to Multi-affine Systems. In: Alur, R., Pappas, G.J. (eds) Hybrid Systems: Computation and Control. HSCC 2004. Lecture Notes in Computer Science, vol 2993. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24743-2_3

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  • DOI: https://doi.org/10.1007/978-3-540-24743-2_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21259-1

  • Online ISBN: 978-3-540-24743-2

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