Skip to main content

Path-Dependent Impulse and Hybrid Systems

  • Conference paper
  • First Online:
Hybrid Systems: Computation and Control (HSCC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2034))

Included in the following conference series:

  • 1545 Accesses

Abstract

Path-dependent impulse differential inclusions, and in particular, path-dependent hybrid control systems, are defined by a path-dependent differential inclusion (or path-dependent control system, or differential inclusion and control systems with memory) and a path-dependent reset map.

In this paper, we characterize the viability property of a closed subset of paths under an impulse path-dependent differential inclusion using the Viability Theorems for path-dependent differential inclusions.

Actually, one of the characterizations of the Characterization Theorem is valid for any general impulse evolutionary system that we shall defined in this paper.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. AUBIN J.-P. (1991) Viability Theory Birkhäuser, Boston, Basel, Berlin

    Google Scholar 

  2. AUBIN J.-P. (1999) Impulse Differential Inclusions and Hybrid Systems:A Viability Approach, Lecture Notes, University of California at Berkeley

    Google Scholar 

  3. AUBIN J.-P. (2000) Lyapunov Functions for Impulse and Hybrid Control Systems, Proceedings of the CDC 2000 Conference

    Google Scholar 

  4. AUBIN J.-P. (2000) Optimal Impulse Control Problems and Quasi-Variational Inequalities Thirty Years Later: a Viability Approach, in Contrôle optimal et EDP: Innovations et Applications, IOS Pressf

    Google Scholar 

  5. AUBIN J.-P. (to appear) Viability Kernels and Capture Basins of Sets under Differential Inclusions, SIAM J. Control

    Google Scholar 

  6. AUBIN J.-P. & FRANKOWSKA H. (1990) Set-Valued Analysis, Birkhäuser, Boston, Basel, Berlin

    Google Scholar 

  7. AUBIN J.-P. & HADDAD G. (to appear) Cadenced runs of impulse and hybrid control systems, International Journal Robust and Nonlinear Control

    Google Scholar 

  8. AUBIN J.-P., LYGEROS J., QUINCAMPOIX M., SASTRY S. & SEUBE N. (to appear) Impulse Differential Inclusions: A Viability Approach to Hybrid Systems

    Google Scholar 

  9. BENSOUSSAN A. & MENALDI (1997) Hybrid Control and Dynamic Programming, Dynamics of Continuous, Discrete and Impulse Systems, 3, 395–442

    MATH  MathSciNet  Google Scholar 

  10. BRANICKY M.S., BORKAR V.S. & MITTER S. (1998) A unified framework for hybrid control: Background, model and theory, IEEE Trans. Autom. Control, 43, 31–45

    Article  MATH  MathSciNet  Google Scholar 

  11. CARDALIAGUET P., UINCAMPOIX M. & SAINT-PIERRE P. (1994) Temps optimaux pour des problèmes avec contraintes et sans contrôlabilité locale Comptes-Rendus de l’Académie des Sciences, Série 1, Paris, 318, 607–612

    Google Scholar 

  12. HADDAD G. (1981) Monotone trajectories of differential inclusions with memory, Isr. J. Math., 39, 83–100

    Article  MATH  MathSciNet  Google Scholar 

  13. HADDAD G. (1981) Monotone viable trajectories for functional differential inclusions, J. Diff. Eq., 42, 1–24

    Article  MATH  MathSciNet  Google Scholar 

  14. HADDAD G. (1981) Topological properties of the set of solutions for functional differential differential inclusions, Nonlinear Anal. Theory, Meth. Appl., 5, 1349–1366

    Article  MATH  MathSciNet  Google Scholar 

  15. MATVEEV A.S., SAVKIN A.V. (2000) Qualitative Theory of Hybrid Dynamical Systems, Birkhäuser

    Google Scholar 

  16. MATVEEV A.S., SAVKIN A.V. (2001) Hybrid dynamical systems: Controller and sensor switching problems, Birkhäuser

    Google Scholar 

  17. ROCKAFELLAR R.T. & WETS R. (1997) Variational Analysis, Springer-Verlag

    Google Scholar 

  18. SHAFT (van der) A. & SCHUMACHER H. (1999) An introduction to hybrid dynamical systems, Springer-Verlag, Lecture Notes in Control, 251

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Aubin, JP., Haddad, G. (2001). Path-Dependent Impulse and Hybrid Systems. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A. (eds) Hybrid Systems: Computation and Control. HSCC 2001. Lecture Notes in Computer Science, vol 2034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45351-2_13

Download citation

  • DOI: https://doi.org/10.1007/3-540-45351-2_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41866-5

  • Online ISBN: 978-3-540-45351-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics