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International Workshop on Hybrid Systems: Computation and Control

HSCC 2006: Hybrid Systems: Computation and Control pp 257–271Cite as

Efficient Computation of Reachable Sets of Linear Time-Invariant Systems with Inputs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3927))

Abstract

This work is concerned with the problem of computing the set of reachable states for linear time-invariant systems with bounded inputs. Our main contribution is a novel algorithm which improves significantly the computational complexity of reachability analysis. Algorithms to compute over and under-approximations of the reachable sets are proposed as well. These algorithms are not subject to the wrapping effect and therefore our approximations are tight. We show that these approximations are useful in the context of hybrid systems verification and control synthesis. The performance of a prototype implementation of the algorithm confirms its qualities and gives hope for scaling up verification technology for continuous and hybrid systems.

This work was partially supported by the European Community projects IST-2001-33520 CC (Control and Computation) and IST-2003-507219 PROSYD (Property-based System Design) as well as by the project CalCel of région Rhône-Alpes.

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Author information

Authors and Affiliations

  1. Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, 19104, USA

    Antoine Girard

  2. École Normale Supérieure, 45 rue d’Ulm, 75005, Paris, France

    Colas Le Guernic

  3. VERIMAG, 2 avenue de Vignate, 38610, Gières, France

    Oded Maler

Authors
  1. Antoine Girard
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  2. Colas Le Guernic
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  3. Oded Maler
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Editor information

Editors and Affiliations

  1. Center for Control, Dynamical Systems and Computation, University of California, 93106, Santa Barbara, CA, USA

    João P. Hespanha

  2. SRI International, 333 Ravenswood Ave, Menlo Park, CA, USA

    Ashish Tiwari

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© 2006 Springer-Verlag Berlin Heidelberg

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Girard, A., Le Guernic, C., Maler, O. (2006). Efficient Computation of Reachable Sets of Linear Time-Invariant Systems with Inputs. In: Hespanha, J.P., Tiwari, A. (eds) Hybrid Systems: Computation and Control. HSCC 2006. Lecture Notes in Computer Science, vol 3927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11730637_21

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  • DOI: https://doi.org/10.1007/11730637_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-33170-4

  • Online ISBN: 978-3-540-33171-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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