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The Discrete Time Behavior of Lazy Linear Hybrid Automata

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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 study the class of lazy linear hybrid automata with finite precision. The key features of this class are:

  • The observation of the continuous state and the rate changes associated with mode switchings take place with bounded delays.

  • The values of the continuous variables can be observed with only finite precision.

  • The guards controlling the transitions of the automaton are finite conjunctions of arbitrary linear constraints.

We show that the discrete time dynamics of this class of automata can be effectively analyzed without requiring resetting of the continuous variables during mode changes. In fact, our result holds for guard languages that go well beyond linear constraints.

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References

  1. Alur, R., Henzinger, T., Lafferriere, G., Pappas, G.: Discrete abstractions of hybrid systems. Proc. of the IEEE 88, 971–984 (2000)

    Article  Google Scholar 

  2. Henzinger, T.: The theory of hybrid automata. In: 11th LICS, pp. 278–292. IEEE Press, Los Alamitos (1996)

    Google Scholar 

  3. Asarin, E., Maler, O.: Achilles and the tortoise climbing up the arithmetical hierarchy. J. of Comp. and Sys. Sci. 57, 389–398 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  4. Asarin, E., Maler, O., Pnueli, A.: Reachability analysis of dynamical systems having piecewise-constant derivatives. Theoretical Comp. Sci. 138, 35–65 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  5. Blondel, V., Tsitsiklis, J.: Complexity of stability and controllability of elementary hybrid systems. Automatica 35, 479–489 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  6. Blondel, V., Bournez, O., Koiran, P., Papdamitrou, C., Tsitsiklis, J.: Deciding stability and mortality of piecewise affine dynamical systems. Theoretical Comp. Sci. 255, 687–696 (2001)

    Article  MATH  Google Scholar 

  7. Henzinger, T., Kopke, P., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? J. of Comp. and Sys. Sci. 57, 94–124 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  8. Henzinger, T.: Hybrid automata with finite bisimulations. In: Fülöp, Z., Gecseg, F. (eds.) ICALP 1995. LNCS, vol. 944, pp. 324–335. Springer, Heidelberg (1995)

    Google Scholar 

  9. Kesten, Y., Pnueli, A., Sifakis, J., Yovine, S.: Integration graphs: A class of decidable hybrid systems. In: Grossman, R.L., Ravn, A.P., Rischel, H., Nerode, A. (eds.) HS 1991 and HS 1992. LNCS, vol. 736, pp. 179–208. Springer, Heidelberg (1993)

    Google Scholar 

  10. McManis, J., Varaiya, P.: Suspension automata: A decidable class of hybrid automata. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 105–117. Springer, Heidelberg (1994)

    Google Scholar 

  11. Puri, A., Varaiya, P.: Decidability of hybrid systems with rectangular differential inclusions. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 95–104. Springer, Heidelberg (1994)

    Google Scholar 

  12. Agrawal, M., Thiagarajan, P.S.: Lazy rectangular hybrid automata. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 1–15. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  13. Henzinger, T., Kopke, P.: Discrete-time control for rectangular hybrid automata. Theoretical Comp. Sci. 221, 369–392 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  14. Gupta, V., Henzinger, T., Jagadeesan, R.: Robust timed automata. In: Maler, O. (ed.) HART 1997. LNCS, vol. 1201, pp. 331–345. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  15. Henzinger, T., Raskin, J.F.: Robust undecidability of timed and hybrid systems. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 145–159. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  16. Ouaknine, J., Worrell, J.: Revisiting digitization, robustness and decidability for timed automata. In: 25th LICS, pp. 198–207. IEEE Press, Los Alamitos (2003)

    Google Scholar 

  17. Alur, R., Dill, D.: A theory of timed automata. Theoretical Comp. Sci. 126, 183–235 (1994)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Computing, National University of Singapore,  

    Manindra Agrawal & P. S. Thiagarajan

Authors
  1. Manindra Agrawal
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  2. P. S. Thiagarajan
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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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Agrawal, M., Thiagarajan, P.S. (2005). The Discrete Time Behavior of Lazy Linear Hybrid Automata. 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_4

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  • DOI: https://doi.org/10.1007/978-3-540-31954-2_4

  • 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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