Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Hybrid Systems: Computation and Control

HSCC 2000: Hybrid Systems: Computation and Control pp 73–88Cite as

Verification of Hybrid Systems with Linear Differential Inclusions Using Ellipsoidal Approximations

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1790))

Abstract

A general verification algorithm is described. It is then shown how ellipsoidal methods developed by A. B. Kurzhanski and P. Varaiya can be adapted to the algorithm. New numerical algorithms that compute approximations of unions of ellipsoids and intersections of ellipsoids and polyhedra were developed. The presented techniques were implemented in the verification tool called VeriSHIFT and some practical results are discussed.

Research supported by National Science Foundation Grant ECS 9725148 and ONR Contract 11

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Botchkarev O., Ellipsoidal Techniques for Verification of Hybrid Systems, 2000. Available at: http://robotics.eecs.berkeley.edu/~olegb/VeriSHIFT/.

  2. Dang T. and Maler O., Reachability Analysis via Face Lifting. In T.A. Henzinger and S. Sastry (Eds), Hybrid Systems: Computation and Control, 96–109, LNCS 1386, Springer, 1998.

    Google Scholar 

  3. Henzinger T, Ho P. and Wong-Toi H., HyTech: A Model Checker for Hybrid Systems. In Software Tools for Technology Transfer, 1, 1997.

    Google Scholar 

  4. Kurzhanski A. B. and Filippova T. F., On the Theory of Trajectory Tubes: a Mathematical Formalism for Uncertain Dynamics, Viability and Control, in: Advances in Nonlinear Dynamics and Control, ser. PSCT 17, pp.122–188, Birkhäuser, Boston, 1993.

    Google Scholar 

  5. Kurzhanski A. B. and Vályi I. Ellipsoidal Calculus for Estimation and Control, Birkhäuser, Boston, ser.SCFA, 1996.

    Google Scholar 

  6. Kurzhanski A. B. and Varaiya P., Ellipsoidal Techniques for Reachability Analysis, 2000. Proceedings of this conference.

    Google Scholar 

  7. Puri A., Borkar V. and Varaiya P., ∈-Approximations of Differential Inclusions, in: R. Alur, T.A. Henzinger, and E.D. Sonntag eds., Hybrid Systems, pp. 109–123, LNCS 1201, Springer, 1996.

    Google Scholar 

  8. Puri A. and Varaiya P., Decidability of Hybrid Systems with Rectangular Differential Inclusions, in D. Dill ed., Proc. CAV’94, LNCS 1066, Springer, 1966.

    Google Scholar 

  9. Rockafellar, R. T., Convex Analysis, Princeton University Press, 1970.

    Google Scholar 

  10. Varaiya P., Reach Set Computation Using Optimal Control, in Proc.of KIT Workshop on Verification of Hybrid Systems, Verimag, Grenoble, 1998.

    Google Scholar 

  11. VeriSHIFT Home Page. http://robotics.EECS.Berkeley.EDU/~olegb/VeriSHIFT/.

  12. Ye Y., On Affine Scaling Algorithms for Non-Convex Quadratic Programming. In Mathematical Programming, 56(1992), pp. 285–300.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The University of California at Berkeley, 195M Cory Hall, Berkeley, CA, 94720

    Oleg Botchkarev & Stavros Tripakis

Authors
  1. Oleg Botchkarev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stavros Tripakis
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Nancy Lynch

  2. Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, 15235, USA

    Bruce H. Krogh

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Botchkarev, O., Tripakis, S. (2000). Verification of Hybrid Systems with Linear Differential Inclusions Using Ellipsoidal Approximations. In: Lynch, N., Krogh, B.H. (eds) Hybrid Systems: Computation and Control. HSCC 2000. Lecture Notes in Computer Science, vol 1790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46430-1_10

Download citation

  • DOI: https://doi.org/10.1007/3-540-46430-1_10

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67259-3

  • Online ISBN: 978-3-540-46430-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation