Skip to main content

Analyzing and synthesizing hybrid control systems

  • Formal Model and Analysis
  • Chapter
  • First Online:
Lectures on Embedded Systems (EEF School 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1494))

Included in the following conference series:

Abstract

Embedded systems possess a hybrid structure, combining continuous-variable dynamics and logical decision-making. We study such real-world hybrid control systems and introduce a mathematical model of them. Then, we develop tools for analyzing their stability. Finally, we review the theory of optimal hybrid control and present algorithms for synthesizing optimal hybrid control 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. Panos J. Antsaklis, James A. Stiver, and Michael D. Lemmon. Hybrid system modeling and autonomous control systems. In Grossman et al. [24], pages 366–392.

    Google Scholar 

  2. Karl J. Åström. Course notes on nonlinear systems. Lund Institute of Technology, 1968.

    Google Scholar 

  3. Allen Back, John Guckenheimer, and Mark Myers. A dynamical simulation facility for hybrid systems. In Grossman et al. [24], pages 255–267.

    Google Scholar 

  4. Dimitur D. Bainov and Pavel S. Simeonov. Systems with Impulse Effect. Ellis Horwood, Chichester, England, 1989.

    Google Scholar 

  5. Alain Bensoussan and Jacques-Louis Lions. Impulse Control and Quasi-VariationalInequalities. Gauthier-Villars, Paris, 1984.

    Google Scholar 

  6. Dmitri P. Bertsekas. Dynamic Programming: Deterministic and Stochastic Models. Prentice Hall, Englewood Cliffs, NJ, 1987.

    Google Scholar 

  7. Michael S. Branicky. Topology of hybrid systems. In Proc. IEEE Conf. Decision and Control, pages 2309–2314, San Antonio, December 1993.

    Google Scholar 

  8. Michael S. Branicky. Analyzing continuous switching systems: Theory and examples. In Proc. American Control Conf., pages 3110–3114, Baltimore, June 1994.

    Google Scholar 

  9. Michael S. Branicky. Continuity of ODE solutions. Applied Mathematics Letters, 7(5):57–60, 1994.

    Google Scholar 

  10. Michael S. Branicky. Stability of switched and hybrid systems. In Proc. IEEE Conf. Decision and Control, pages 3498–3503, Lake Buena Vista, FL, December 1994.

    Google Scholar 

  11. Michael S. Branicky. Studies in Hybrid Systems: Modeling, Analysis, and Control. PhD thesis, Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, June 1995.

    Google Scholar 

  12. Michael S. Branicky. Universal computation and other capabilities of hybrid and continuous dynamical systems. Theoretical Computer Science, 138(1):67–100, 1995.

    Google Scholar 

  13. Michael S. Branicky. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Transactions on Automatic Control, April 1998. In press.

    Google Scholar 

  14. Michael S. Branicky, Vivek Borkar, and Sanjoy K. Mitter. A unified framework for hybrid control. Technical Report LIDS-P-2239, Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, April 1994. Extended abstract in [16]. Summary and examples in [15].

    Google Scholar 

  15. Michael S. Branicky, Vivek S. Borkar, and Sanjoy K. Mitter. A unified framework for hybrid control. In Proc. IEEE Conf. Decision and Control, pages 4228–4234, Lake Buena Vista, FL, December 1994.

    Google Scholar 

  16. Michael S. Branicky, Vivek S. Borkar, and Sanjoy K. Mitter. A unified framework for hybrid control. In G. Cohen and J-P. Quadrat, editors, Proceedings 11th INRIA International Conference on the Analysis and Optimization of Systems, volume 199 of Lecture Notes in Control and Information Sciences, pages 352–358, New York, 1994. Springer-Verlag. Extended Abstract.

    Google Scholar 

  17. Michael S. Branicky, Vivek S. Borkar, and Sanjoy K. Mitter. A unified framework for hybird control: Model and optimal control theory. IEEE Transactions on Automatic Control, pages 31–45, January 1998.

    Google Scholar 

  18. Michael S. Branicky and Sven Erik Mattsson. Simulation of hybrid systems. In Panos J. Antsaklis, Wolf Kohn, Anil Nerode, and Shankar Sastry, editors, Hybrid Systems IV, volume 1273 of Lecture Notes in Computer Science, pages 31–56. Springer-Verlag, New York, 1997.

    Google Scholar 

  19. Michael S. Branicky and Sanjoy K. Mitter. Algorithms for optimal hybrid control. In Proc. IEEE Conf. Decision and Control, New Orleans, December 1995. 2661–2666.

    Google Scholar 

  20. Roger W. Brockett. Hybrid models for motion control systems. In H. L. Trentelman and J. C. Willems, editors, Essays in Control: Perspectives in the Theory and its Applications, pages 29–53. Birkhäuser, Boston, 1993.

    Google Scholar 

  21. Chee-Seng Chow and John N. Tsitsiklis. An optimal one-way multigrid algorithm for discrete-time stochastic control. IEEE Trans. Automatic Control, 36(8):898–914, 1991.

    Google Scholar 

  22. O. L. V. Costa and M. H. A. Davis. Impulse control of piecewise deterministic processes. Math. Control Signals Syst., 2:187–206, 1989.

    Google Scholar 

  23. Akash Deshpande. Control of Hybrid Systems. PhD thesis, University of California at Berkeley, Dept. of Electrical Engineering and Computer Science, 1994.

    Google Scholar 

  24. Robert L. Grossman, Anil Nerode, Anders P. Ravn, and Hans Rischel, editors. Hybrid Systems, volume 736 of Lecture Notes in Computer Science. Springer-Verlag, New York, 1993.

    Google Scholar 

  25. David Harel. Statecharts: A visual formalism for complex systems. Science of Computer Programming, 8:231–274, 1987.

    Google Scholar 

  26. Morris W. Hirsch and Stephen Smale. Differential Equations, Dynamical Systems, and Linear Algebra. Academic Press, San Diego, 1974.

    Google Scholar 

  27. Yu-Chi Ho, editor. Discrete Event Dynamic Systems. Analyzing Complexity and Performance in the Modern World. IEEE Press, Piscataway, NJ, 1992.

    Google Scholar 

  28. Mikael Johansson and Anders Rantzer. Computation of piecewise quadratic Lyapunov functions for hybrid systems. Internal Report TFRT-7549, Department of Automatic Control, Lund Institute of Technology, June 1996. Submitted for journal publication.

    Google Scholar 

  29. David G. Luenberger. Introduction to Dynamic Systems: Theory, Models, and Applications. Wiley, New York, 1979.

    Google Scholar 

  30. Jorgen Malmborg, Bo Bernhardsson, and Karl J. Åström. A stabilizing switching scheme for multi-controller systems. In Proc. IFAC World Congress, page to appear, San Francisco, July 1996.

    Google Scholar 

  31. George Meyer. Design of flight vehicle management systems. In Proc. IEEE Conf. Decision and Control, Lake Buena Vista, FL, December 1994. Plenary Lecture.

    Google Scholar 

  32. Sanjoy K. Mitter and Shankar Sastry. 6.291; Special Topics: Intelligent Control. Course Notes, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Fall 1992.

    Google Scholar 

  33. Anil Nerode and Wolf Kohn. Models for hybrid systems: Automata, topologies, stability. In Grossman et al. [24], pages 317–356.

    Google Scholar 

  34. Theodosios Pavlidis. Stability of systems described by differential equations containing impulses. IEEE Trans. Automatic Control, 12(1):43–45, 1967.

    Google Scholar 

  35. Philippos Peleties and Raymond DeCarlo. Asymptotic stability of m-switched systems using Lyapunov-like functions. In Proc. American Control Conf., pages 1679–1684, Boston, June 1991.

    Google Scholar 

  36. Stefan Pettersson and Bengt Lennartson. Modelling, analysis, and synthesis of hybrid systems. In Preprints of the Reglermöte, Lulea, Sweden, June 1996.

    Google Scholar 

  37. Marc H. Raibert. Legged Robots that Balance. MIT Press, Cambridge, MA, 1986.

    Google Scholar 

  38. Sheldon M. Ross. Applied Probability Models with Optimization Applications. Dover, New York, 1992.

    Google Scholar 

  39. Konstantin S. Sibirsky. Introduction to Topological Dynamics. Noordhoff International Publishing, Leyden, The Netherlands, 1975. Translated by Leo F. Boron.

    Google Scholar 

  40. Jean-Jacques E. Slotine and Weiping Li. Applied Nonlinear Control. Prentice-Hall, Englewood Cliffs, NJ, 1991.

    Google Scholar 

  41. Eduardo D. Sontag. Mathematical Control Theory: Deterministic Finite Dimensional Systems, volume 6 of Texts in Applied Mathematics. Springer-Verlag, New York, 1990.

    Google Scholar 

  42. Lucio Tavernini. Differential automata and their discrete simulators. Nonlinear Analysis, Theory, Methods, and Applications, 11(6):665–683, 1987.

    Google Scholar 

  43. Vadim I. Utkin. Variable structure systems with sliding modes. IEEE Trans. Automatic Control, 22(2):212–222, 1977.

    Google Scholar 

  44. Pravin P. Varaiya. Smart cars on smart roads: Problems of control. IEEE Trans. Automatic Control, 38(2):195–207, February 1993.

    Google Scholar 

  45. Mathukumalli Vidyasagar. Nonlinear Systems Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1978. Also: 2nd Edition, 1993.

    Google Scholar 

  46. Jacques Leopold Willems. Stability Theory of Dynamical Systems. Nelson, Loudon, 1970.

    Google Scholar 

  47. Hans S. Witsenhausen. A class of hybrid-state continuous-time dynamic systems. IEEE Trans. Automatic Control, 11(2):161–167, 1966.

    Google Scholar 

  48. Hui Ye, Anthony N. Michel, and Ling Hou. Stability theory for hybrid dynamical systems. In Proc. IEEE Conf. Decision and Control, pages 2679–2684, New Orleans, December 1995.

    Google Scholar 

  49. Laurence Chisolm Young. Lectures on the Calculus of Variations and Optimal Control Theory. Chelsea, New York, 2nd edition, 1980.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Grzegorz Rozenberg Frits W. Vaandrager

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Branicky, M.S. (1998). Analyzing and synthesizing hybrid control systems. In: Rozenberg, G., Vaandrager, F.W. (eds) Lectures on Embedded Systems. EEF School 1996. Lecture Notes in Computer Science, vol 1494. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-65193-4_19

Download citation

  • DOI: https://doi.org/10.1007/3-540-65193-4_19

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65193-2

  • Online ISBN: 978-3-540-49498-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics