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Generating Polynomial Invariants for Hybrid Systems

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Hybrid Systems: Computation and Control (HSCC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3414))

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Abstract

We present a powerful computational method for automatically generating polynomial invariants of hybrid systems with linear continuous dynamics. When restricted to linear continuous dynamical systems, our method generates a set of polynomial equations (algebraic set) that is the best such over-approximation of the reach set. This shows that the set of algebraic invariants of a linear system is computable. The extension to hybrid systems is achieved using the abstract interpretation framework over the lattice defined by algebraic sets. Algebraic sets are represented using canonical Gröbner bases and the lattice operations are effectively computed via appropriate Gröbner basis manipulations.

The research of the first author was partially supported by Spanish FPU grant ref. AP2002-3693 and the projects Maverish (MCYT TIC2001-2476-C03-01) and LogicTools (TIN2004-03382) funded by the Spanish Ministry of Education and Science. The second author was supported in part by the National Science Foundation under grants CCR-0311348 and CCR-ITR-0326540 and NASA Langley Research Center contract NAS1-00108 to Rannoch Corporation.

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Author information

Authors and Affiliations

  1. LSI Department, Technical University of Catalonia, Jordi Girona, 1-3, 08034, Barcelona, Spain

    Enric Rodríguez-Carbonell

  2. SRI International, 333 Ravenswood Ave, Menlo Park, CA, U.S.A.

    Ashish Tiwari

Authors
  1. Enric Rodríguez-Carbonell
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  2. Ashish Tiwari
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Editor information

Editors and Affiliations

  1. Automatic Control Laboratory, ETH Zurich, 8092, Zurich, Switzerland

    Manfred Morari

  2. Computer Engineering and Networks Laboratory, ETH Zurich, Switzerland

    Lothar Thiele

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Rodríguez-Carbonell, E., Tiwari, A. (2005). Generating Polynomial Invariants for Hybrid Systems. In: Morari, M., Thiele, L. (eds) Hybrid Systems: Computation and Control. HSCC 2005. Lecture Notes in Computer Science, vol 3414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31954-2_38

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  • DOI: https://doi.org/10.1007/978-3-540-31954-2_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25108-8

  • Online ISBN: 978-3-540-31954-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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