Advertisement

Composing Reachability Analyses of Hybrid Systems for Safety and Stability

  • Sergiy Bogomolov
  • Corina Mitrohin
  • Andreas Podelski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6252)

Abstract

We present a method to enhance the power of a given reachability analysis engine for hybrid systems. The method works by a new form of composition of reachability analyses, each on a different relaxation of the input hybrid system. We present preliminary experiments that indicate its practical potential for checking safety and stability.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alur, R., Grosu, R., Hur, Y., Kumar, V., Lee, I.: Modular specification of hybrid systems in CHARON. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 6–19. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  2. 2.
    Asarin, E., Dang, T.: Abstraction by projection and application to multi-affine systems. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 32–47. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
  4. 4.
    Frehse, G.: PHAVer: Algorithmic verification of hybrid systems past HyTech. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 258–273. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Henzinger, T.A., Ho, P.-H.: Algorithmic analysis of nonlinear hybrid systems. In: Wolper, P. (ed.) CAV 1995. LNCS, vol. 939, pp. 225–238. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  6. 6.
    Henzinger, T.A., Ho, P.-H., Wong-Toi, H.: HyTech: A model checker for hybrid systems. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 460–463. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  7. 7.
    Hespanha, J.P., Morse, A.S.: Stability of switched systems with average dwell-time. In: Decision and Control (1999)Google Scholar
  8. 8.
    Jha, S.K., Krogh, B.H., Weimer, J.E., Clarke, E.M.: Reachability for linear hybrid automata using iterative relaxation abstraction. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 287–300. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Maler, O., Batt, G.: Approximating continuous systems by timed automata. In: Fisher, J. (ed.) FMSB 2008. LNCS (LNBI), vol. 5054, pp. 77–89. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Mitra, S., Liberzon, D., Lynch, N.A.: Verifying average dwell time of hybrid systems. ACM Trans. Embedded Comput. Syst. 8(1) (2008)Google Scholar
  11. 11.
    Podelski, A., Wagner, S.: Model checking of hybrid systems: From reachability towards stability. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 507–521. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Podelski, A., Wagner, S.: Region stability proofs for hybrid systems. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 320–335. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Podelski, A., Wagner, S.: A sound and complete proof rule for region stability of hybrid systems. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 750–753. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  14. 14.
    Puri, A., Varaiya, P.: Verification of hybrid systems using abstractions. In: Hybrid Systems II, pp. 359–369. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  15. 15.
    Silva, B.I., Richeson, K., Krogh, B.H., Chutinan, A.: Modeling and verification of hybrid dynamical system using CheckMate. In: ADPM (2000)Google Scholar
  16. 16.
    Stursberg, O., Kowalewski, S., Engell, S.: On the generation of timed discrete approximations for continuous systems. Mathematical and Computer Modeling of Dynamical Systems 6(1), 51–70 (2000)CrossRefzbMATHGoogle Scholar
  17. 17.
    Torrisi, F.D., Bemporad, A.: Hysdel — a tool for generating computational hybrid models for analysis and synthesis problems. IEEE Transactions on Control Systems Technology 12 (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Sergiy Bogomolov
    • 1
  • Corina Mitrohin
    • 1
  • Andreas Podelski
    • 1
  1. 1.Department of Computer ScienceUniversity of FreiburgFreiburgGermany

Personalised recommendations