Skip to main content

Optimal Control Using Bisimulations: Implementation

  • 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:

Abstract

We consider the synthesis of optimal controls for continuous feedback systems by recasting the problem to a hybrid optimal control problem which is to synthesize optimal enabling conditions for switching between locations in which the control is constant. We provide a single- pass algorithm to solve the dynamic programming problem that arises, with added constraints to ensure non-Zeno trajectories.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Broucke. A geometric approach to bisimulation and verification of hybrid systems. In Hybrid Systems: Computation and Control, F. Vaandrager and J. van Schuppen, eds., LNCS 1569, Springer-Verlag, pp. 61–75, 1999.

    Chapter  Google Scholar 

  2. M. Broucke, M.D. Di Benedetto, S. Di Gennaro, A. Sangiovanni-Vincentelli. Theory of optimal control using bisimulations. In Hybrid Systems: Computation and Control, N. Lynch and B. Krogh, eds., LNCS 1790, Springer-Verlag, pp. 89–102, 2000.

    Chapter  Google Scholar 

  3. I. Capuzzo Dolcetta. On a discrete approximation of the Hamilton-Jacobi equation for dynamic programming. Applied Math. Optim., vol. 10, pp. 367–377, 1983.

    Article  MathSciNet  Google Scholar 

  4. M.G. Crandall, P.L. Lions. Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc., vol. 277, no. 1, pp. 1–42, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  5. M.G. Crandall, P.L. Lions. Two approximations of solutions of Hamilton-Jacobi equations. Mathematics of Computation, vol. 43, no. 176, pp. 1–19, July 1984.

    Article  MATH  MathSciNet  Google Scholar 

  6. E.W. Dijkstra. A note on two problems in connection with graphs. Numerische Mathematik 1, p. 269–271, 1959.

    Article  MATH  MathSciNet  Google Scholar 

  7. M. Falcone. A numerical approach to the infinite horizon problem of deterministic control theory. Applied Mathematics and Optimization, 15, pp. 1–13, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  8. W.H. Fleming, R.W. Rishel. Deterministic and stochastic optimal control. Springer-Verlag, New York, 1975.

    MATH  Google Scholar 

  9. R. Gonzales and E. Rofman. On deterministic control problems: an approximation procedure for the optimal cost. I: the stationary problem. SIAM J. Contr. Optim., vol. 23, no. 2, pp. 242–266, 1985.

    Article  Google Scholar 

  10. P.L. Lions. Generalized solutions of Hamilton-Jacobi equations. Pitman, Boston, 1982.

    Google Scholar 

  11. E. Asarin and O. Maler. As soon as possible: time optimal control for timed automata. In Hybrid Systems: Computation and Control, F. Vaandrager and J. van Schuppen, eds., LNCS 1569, Springer-Verlag, pp. 19–30, 1999.

    Chapter  Google Scholar 

  12. L. Polymenakos, D. Bertsekas, and J. Tsitsiklis. Implementation of efficient algorithms for globally optimal trajectories. IEEE Trans. AC, vol.43, no.2, pp. 278–83, Feb. 1998.

    MATH  MathSciNet  Google Scholar 

  13. P.E. Souganidis. Approximation schemes for viscosity solutions of Hamilton-Jacobi equations. Journal of Differential Equations, vol. 59, no. 1, p. 1–43, August 1985.

    Article  MATH  MathSciNet  Google Scholar 

  14. J.N. Tsitsiklis. Efficient algorithms for globally optimal trajectories. IEEE Transactions on Automatic Control, vol. 40, no. 9, pp. 1528–1538, September 1995.

    Article  MATH  MathSciNet  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

Broucke, M., Di Benedetto, M.D., Di Gennaro, S., Sangiovanni-Vincentelli, A. (2001). Optimal Control Using Bisimulations: Implementation. 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_17

Download citation

  • DOI: https://doi.org/10.1007/3-540-45351-2_17

  • 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