Skip to main content

Abstract verification of structured dynamical systems

  • Conference paper
  • First Online:
Hybrid Systems III (HS 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1066))

Included in the following conference series:

Abstract

Dynamical systems combining different kinds of time are analyzed with the help of homomorphisms which allow time abstraction besides the usual state abstraction and which do preserve fundamental temporal properties. Dynamical systems are composed by restriction, union, synchronization, concatenation and iteration. Thanks to abstraction and structure, the qualitative analysis of systems which are hard to understand can be reduced to that of simpler, homomorphic systems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akin, E., The General Topology of Dynamical Systems, American Math. Soc., Providence, 1993.

    Google Scholar 

  2. Alur, R., et al., The algorithmic analysis of hybrid systems, Theor. Computer Sci. 138(1995) 3–34.

    Article  Google Scholar 

  3. Alfaro, L. de, and Z. Manna, Verification in continuous time by discrete time reasoning, in: V.S. Alagar and M. Nivat (eds.), Algebraic Methodology and Software Technology, LNCS 936, Springer, Berlin, 1995, pp. 292–306.

    Google Scholar 

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

    Article  Google Scholar 

  5. Alpern, B., and F.B. Schneider, Defining liveness, Information Proc. Letters 21(1985) 181–186.

    Article  Google Scholar 

  6. Benveniste, A., M. Le Borgne and P. Le Guernic, Hybrid systems: the Signal approach, in: R.L. Grossman et al. (eds.), Hybrid Systems, LNCS 736, Springer, Berlin, 1992, pp. 230–254.

    Google Scholar 

  7. Collette, P., Design of Compositional Proof Systems — Application to Unity, Ph.D. thesis, U. Louvain, 1994.

    Google Scholar 

  8. Dijkstra, E.W., A Discipline of Programming, Prentice-Hall, Englewood Cliffs, 1976.

    Google Scholar 

  9. Geurts, F., Compositional complexity in dynamical systems, RR95-14, Dept Computing Sci. and Eng., U. Louvain. Also in: Proc. 1995 Intl Symp. on Nonlinear Theory and its Applications, IEICE, Tokyo, 1995.

    Google Scholar 

  10. Ginzburg, A., Algebraic Theory of Automata, Academic Press, New York, 1968.

    Google Scholar 

  11. Guckenheimer, J., A robust hybrid stabilization strategy for equilibria, IEEE Trans. Automatic Control 40(1995) 321–326.

    Article  Google Scholar 

  12. Hedlung, G.A., Endomorphisms and automorphisms of the shift dynamical system, Math. Systems Theory 3(1969) 320–375.

    Article  Google Scholar 

  13. Kumar, R., V. Garg and S.I. Marcus, Predicates and predicate transformers for supervisory control of discrete event dynamical systems, IEEE Trans. Automatic Control 38(1993) 232–247.

    Article  Google Scholar 

  14. Kwiatkowska, M.Z., On topological characterization of behavioural properties, in: G.M. Reed et al. (eds), Topology and Category Theory in Computer Science, Oxford Sci. Publ., 1991, 153–177.

    Google Scholar 

  15. Lamport, L., What good is temporal logic?, in: R. Mason (ed.), Information Processing 83, North-Holland, Amsterdam, 1983, pp. 657–668.

    Google Scholar 

  16. Mazurkiewicz, A., Introduction to trace theory, in: V. Diekert and G. Rozenberg (eds.), The Book of Traces, World Scientific, Singapore, 1995.

    Google Scholar 

  17. Maler, O., Z. Manna and A. Pnueli, From timed to hybrid systems, in: J.W. de Bakker et al. (eds.), Real Time: Theory and Practice, LNCS 600, Springer, Berlin, 1992, pp. 447–484.

    Google Scholar 

  18. Michel, A.N., and K. Wang, Qualitative Theory of Dynamical Systems, Marcel Dekker, New-York, 1995.

    Google Scholar 

  19. Nerode, A., and W. Kohn, Models of hybrid systems: Automata, topologies, controllability, observability, in: R.L. Grossman et al. (eds.), Hybrid Systems, LNCS 736, Springer, Berlin, 1992, pp. 317–356.

    Google Scholar 

  20. Ramadge, P.J., and W.M. Wonham, Modular feedback logic for discrete-event systems, SIAM J. Control and Optimization 25(1987) 1202–1218.

    Article  Google Scholar 

  21. Sintzoff, M., Invariance and contraction by infinite iterations of relations, in: J.P. Banâtre and D. Le Métayer (eds.), Research Directions in High-Level Parallel Programming Languages, LNCS 574, Springer, Berlin, 1992, pp. 349–373.

    Google Scholar 

  22. Sintzoff, M., Invariance and termination in structured dynamical systems, RR95-13, Dept Computing Sci. and Eng., U. Louvain. Also in: Proc. 1995 Intl Symp. on Nonlinear Theory and its Applications, IEICE, Tokyo, 1995.

    Google Scholar 

  23. Sintzoff, M., and F. Geurts, Analysis of dynamical systems using predicate transformers — Attraction and composition, in: S.I. Andersson (ed.), Analysis of Dynamical and Cognitive Systems, LNCS 888, Springer, Berlin, 1995, pp. 227–260.

    Google Scholar 

  24. Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and Chaos, TAM2, Springer, Berlin, 1990.

    Google Scholar 

  25. Zhang, Y., and A.K. Mackworth, Constraint nets: a semantic model for hybrid dynamic systems, Theor. Computer Sci. 138(1995) 211–239.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Rajeev Alur Thomas A. Henzinger Eduardo D. Sontag

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sintzoff, M. (1996). Abstract verification of structured dynamical systems. In: Alur, R., Henzinger, T.A., Sontag, E.D. (eds) Hybrid Systems III. HS 1995. Lecture Notes in Computer Science, vol 1066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020940

Download citation

  • DOI: https://doi.org/10.1007/BFb0020940

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61155-4

  • Online ISBN: 978-3-540-68334-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics