Reachability Analysis Using Polygonal Projections

  • Mark R. Greenstreet
  • Ian Mitchell
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1569)

Abstract

This paper presents Coho, a reachability analysis tool for systems modeled by non-linear, ordinary differential equations. Coho represents high-dimensional objects using projections onto planes corresponding to pairs of variables. This representation is compact and allows efficient algorithms from computational geometry to be exploited while also capturing dependencies in the behaviour of related variables. Reachability is performed by integration where methods from linear programming and linear systems theory are used to bound trajectories emanating from each face of the object. This paper has two contributions: first, we describe the implementation of Coho and, second, we present analysis results obtained by using Coho on several simple models.

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References

  1. ACH+95.
    R. Alur, C. Courcoubetis, N. Halbwachs, et al. The algorithmic analysis of hybrid systems. Theoretical Computer Science, 138:3–34, 1995.MATHCrossRefMathSciNetGoogle Scholar
  2. AG96.
    Kenneth Arnold and James Gosling. The Java Programming Language. Addison-Wesley, 1996.Google Scholar
  3. Bro89.
    R. W. Brockett. Smooth dynamical systems which realize arithmetical and logical operations. In Hendrik Nijmeijer and Johannes M. Schumacher, editors, Three Decades of Mathematical Systems Theory: A Collection of Surveys at the Occasion of the 50th Birthday of J. C. Willems, volume 135 of Lecture Notes in Control and Information Sciences, pages 19–30. Springer, 1989.Google Scholar
  4. DM98.
    Thao Dang and Oded Maler. Reachability analysis via face lifting. In Thomas A. Henzinger and Shankar Sastry, editors, Proceding of the First International Workshop on Hybrid Systems: Computation and Control, pages 96–109, Berkeley, California, April 1998.Google Scholar
  5. GM98.
    Mark R. Greenstreet and Ian Mitchell. Integrating projections. In Thomas A. Henzinger and Shankar Sastry, editors, Proceding of the First International Workshop on Hybrid Systems: Computation and Control, pages 159–174, Berkeley, California, April 1998.Google Scholar
  6. Gre96.
    Mark R. Greenstreet. Verifying safety properties of di_erential equations. In Proceedings of the 1996 Conference on Computer Aided Verification, pages 277–287, New Brunswick, NJ, July 1996.Google Scholar
  7. HS74.
    Morris W. Hirsch and Stephen Smale. Differential Equations, Dynamical Systems, and Linear Algebra. Academic Press, San Diego, CA, 1974.MATHGoogle Scholar
  8. MG96.
    Ian Mitchell and Mark Greenstreet. Proving Newtonian arbiters correct, almost surely. In Proceedings of the Third Workshop on Designing Correct Circuits, Båstad, Sweden, September 1996.Google Scholar
  9. PS85.
    Franco P. Preparata and Michael I. Shamos. Computational Geometry: An Introduction. Texts and Monographs in Computer Science. Springer, 1985.Google Scholar
  10. The92.
    The Mathworks Inc., Natick, Mass. Matlab: High-Performance Numeric Computation and Visualization Software, 1992. http://www.matlab.com.
  11. TPS97.
    Claire Tomlin, George Pappas, and Shankar Sastry. Conflict resolution for air traffic management: A case study in multi-agent hybrid systems. Technical Report UCB/ERL M97/33, Electronics Research Laboratory, University of California, Berkeley, 1997. to appear in IEEE Transactions on Automatic Control.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Mark R. Greenstreet
    • 1
  • Ian Mitchell
    • 2
  1. 1.Department of Computer ScienceUniversity of British ColumbiaVancouverCanada
  2. 2.Scientific Computing and Computational MathematicsStanford UniversityStanfordUSA

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