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Studying Sequences of Jumps in Hybrid Systems to Detect Zeno Phenomenon

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Numerical Software Verification (NSV 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10152))

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Abstract

We propose a numerical analysis of sequences of points of interest associated to the dynamics of hybrid systems. These sequences are made of instants of switching mode or instants when a particular quantity vanishes. This analysis allows one to discover instant of accumulation points, a.k.a. Zeno phenomenon. Some examples are given to show the potential of this approach.

This research was partially supported by the ANR INS Project CAFEIN (ANR-12-INSE-0007).

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References

  1. Alexandre dit Sandretto, J., Chapoutot, A.: DynBEX: a differential constraint library for studying dynamical systems. In: Conference on Hybrid Systems: Computation and Control (HSCC 2016), Vienne, Austria, April 2016

    Google Scholar 

  2. Bouissou, O., Chapoutot, A.: An operational semantics for Simulink’s simulation engine. In: Languages, Compliers, Tools, and Theory for Embedded Systems, pp. 129–138. ACM (2012)

    Google Scholar 

  3. Bouissou, O., Chapoutot, A., Mimram, S.: HySon: precise simulation of hybrid systems with imprecise inputs. In: Rapid System Prototyping. IEEE (2012)

    Google Scholar 

  4. Brezinski, C., Redivo Zaglia, M.: Extrapolation Methods-Theory and Practice. North-Holland, Amsterdam (1991)

    MATH  Google Scholar 

  5. Brezinski, C., Redivo Zaglia, M.: Generalizations of Aitken’s process for accelerating the convergence of sequences. Comput. Appl. Math. 26(2), 171–189 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Esposito, J.M., Kumar, V., Pappas, G.J.: Accurate event detection for simulating hybrid systems. In: Benedetto, M.D., Sangiovanni-Vincentelli, A. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 204–217. Springer, Heidelberg (2001). doi:10.1007/3-540-45351-2_19

    Chapter  Google Scholar 

  7. Goebel, R., Hespanha, J., Teel, A.R., Cai, C., Sanfelice, R.: Hybrid systems: Generalized solutions and robust stability. In: IFAC NOLCOS, pp. 1–12 (2004)

    Google Scholar 

  8. Hairer, E., Nørsett, S.P., Wanner, G.: Solving Ordinary Differential Equations I: Nonstiff Problems. Springer, Heidelberg (1993)

    MATH  Google Scholar 

  9. Henzinger, T.A.: The theory of hybrid automata. In: Symposium on Logic in Computer Science, pp. 278–292. IEEE Computer Society Press (1996)

    Google Scholar 

  10. Konečný, M., Taha, W., Bartha, F.A., Duracz, J., Duracz, A., Ames, A.D.: Enclosing the behavior of a hybrid automaton up to and beyond a zeno point. Nonlinear Anal. Hybrid Syst. 20, 1–20 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  11. Rudin, W.: Principles of Mathematical Analysis. McGraw-Hill, New York (1976)

    MATH  Google Scholar 

  12. Shampine, L., Gladwell, I., Thompson, S.: Solving ODEs with MATLAB. Cambridge Univ. Press, Cambridge (2003)

    Book  MATH  Google Scholar 

  13. Zhang, F., Yeddanapudi, M., Mosterman, P.J.: Zero-crossing location and detection algorithms for hybrid system simulation. In: IFAC World Congress, pp. 7967–7972 (2008)

    Google Scholar 

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Authors and Affiliations

  1. U2IS, ENSTA ParisTech, Université Paris-Saclay, 828 bd des Maréchaux, 91762, Palaiseau Cedex, France

    Alexandre Chapoutot & Julien Alexandre dit Sandretto

Authors
  1. Alexandre Chapoutot
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  2. Julien Alexandre dit Sandretto
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Corresponding author

Correspondence to Alexandre Chapoutot .

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Editors and Affiliations

  1. IST Austria, Klosterneuburg, Austria

    Sergiy Bogomolov

  2. Université de Perpignan, Perpignan, France

    Matthieu Martel

  3. Kansas State University, Manhattan, Kansas, USA

    Pavithra Prabhakar

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Chapoutot, A., Alexandre dit Sandretto, J. (2017). Studying Sequences of Jumps in Hybrid Systems to Detect Zeno Phenomenon. In: Bogomolov, S., Martel, M., Prabhakar, P. (eds) Numerical Software Verification. NSV 2016. Lecture Notes in Computer Science(), vol 10152. Springer, Cham. https://doi.org/10.1007/978-3-319-54292-8_5

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  • DOI: https://doi.org/10.1007/978-3-319-54292-8_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54291-1

  • Online ISBN: 978-3-319-54292-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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