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International Workshop on Computer Algebra in Scientific Computing

CASC 2015: Computer Algebra in Scientific Computing pp 440–456Cite as

Safety Verification of Hybrid Systems Using Certified Multiple Lyapunov-Like Functions

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9301))

Abstract

In this paper, we present an efficient, hybrid numeric-symbolic method for safety verification of hybrid systems. To start with, we introduce a function of state, defined as a multiple Lyapunov-like function, whose time derivative along the trajectories is non-negative only outside of the initial set, such that its zero level set separates the unsafe region from all possible trajectories starting from the given initial set. Then, a numerical multiple Lyapunov-like function is computed by using sum of squares decomposition and semi-definite programming. Afterwards, in order to recover the possible unreliability of our numerical solution, we apply a continued fractions based rational recovery technique to this floating result and then obtain a certified one with rational coefficients, such that exact verification can be assured by this certified multiple Lyapunov-like function. Finally, several examples, together with discussions, are provided to illustrate the tractability and advantages of our method.

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Authors and Affiliations

  1. SKLSDE, LMIB and School of Mathematics and Systems Science, Beihang University, Beijing, China

    Zhikun She, Dan Song & Meilun Li

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  1. Zhikun She
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  2. Dan Song
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  3. Meilun Li
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Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies, Joint Institute of Nuclear Research, Dubna, Russia

    Vladimir P. Gerdt

  2. Institute for Mathematics, Universität Kassel, Kassel, Germany

    Wolfram Koepf

  3. Institut für Mathematik, Universität Kassel, Kassel, Hessen, Germany

    Werner M. Seiler

  4. Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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She, Z., Song, D., Li, M. (2015). Safety Verification of Hybrid Systems Using Certified Multiple Lyapunov-Like Functions. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2015. Lecture Notes in Computer Science(), vol 9301. Springer, Cham. https://doi.org/10.1007/978-3-319-24021-3_32

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  • DOI: https://doi.org/10.1007/978-3-319-24021-3_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24020-6

  • Online ISBN: 978-3-319-24021-3

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