Skip to main content

Part of the book series: Control Engineering ((CONTRENGIN))

Summary

Hybrid systems arise when the continuous and the discrete meet. Combine continuous and discrete inputs, outputs, states, or dynamics, and you have a hybrid system. Particularly, hybrid systems arise from the use of finite-state logic to govern continuous physical processes (as in embedded control systems) or from topological and network constraints interacting with continuous control (as in networked control systems). This chapter provides an introduction to hybrid systems, building them up first from the completely continuous side and then from the completely discrete side. It should be accessible to control theorists and computer scientists alike.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /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
eBook
USD 229.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 299.99
Price excludes VAT (USA)
  • Durable hardcover 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.

Similar content being viewed by others

References

  1. Alur, R., and Dill, D.L. (1994) A theory of timed automata. Theoretical Computer Science, 126:183-235.

    Article  MATH  MathSciNet  Google Scholar 

  2. Alur, R., Courcoubetis, C., Henzinger, T.A., and Ho, P.-H. (1993) Hybrid au-tomata: An algorithmic approach to the specification and verification of hybrid systems. In: Grossman, R., Nerode, A., Ravn, A., and Rischel, H. (eds) (1993) Hybrid Systems, pp. 209-229. Springer, New York.

    Google Scholar 

  3. Antsaklis, P.J., Stiver, J.A., and Lemmon, M.D. (1993) Hybrid system modeling and autonomous control systems. In: Grossman, R., Nerode, A., Ravn, A., and Rischel, H. (eds) Hybrid Systems, pp. 366-392. Springer, New York.

    Google Scholar 

  4. Back, A., Guckenheimer, J., and Myers, M. (1993) A dynamical simulation facility for hybrid systems. In: Grossman, R., Nerode, A., Ravn, A., and Rischel,. H. (eds) (1993) Hybrid Systems, pp. 255-267. Springer, New York.

    Google Scholar 

  5. Bainov, D.D., and Simeonov, P.S. (1989) Systems with Impulse Effect. Ellis Horwood, Chichester, England.

    MATH  Google Scholar 

  6. Bensoussan, A., and Lions, J.-L. (1984) Impulse Control and Quasi-Variational Inequalities. Gauthier-Villars, Paris.

    Google Scholar 

  7. Branicky, M.S. (1995) Studies in Hybrid Systems: Modeling, Analysis, and Control. ScD thesis, Massachusetts Institute of Technology, Cambridge, MA.

    Google Scholar 

  8. Branicky, M.S. (1997) Stability of hybrid systems: State of the art. In: Proc. IEEE Conf. Decision and Control, pp. 120-125, San Diego, CA.

    Google Scholar 

  9. Branicky, M.S. (1998) Analyzing and synthesizing hybrid control systems. In: Rozenberg, G., and Vaandrager, F. (eds) Lectures on Embedded Systems, pp. 74-113. Springer, Berlin.

    Google Scholar 

  10. Branicky, M.S., Borkar, V.S., and Mitter, S.K. (1998) A unified framework for hybrid control: Model and optimal control theory. IEEE Trans. Automatic Control, 43(1):31-45.

    Article  MATH  MathSciNet  Google Scholar 

  11. Branicky, M.S., Hebbar, R., and Zhang, G. (1999) A fast marching algorithm for hybrid systems. In: Proc. IEEE Conf. Decision and Control, pp. 4897-4902. Phoenix, AZ.

    Google Scholar 

  12. Branicky, M.S., and Mattsson, S.E. (1997) Simulation of hybrid systems. In: Antsaklis, P.J., Kohn, W., Nerode, A., and Sastry, S. (eds) Hybrid Systems IV, pp. 31-56. Springer, New York.

    Chapter  Google Scholar 

  13. Branicky, M.S., and Mitter, S.K. (1995) Algorithms for optimal hybrid control. Proc. IEEE Conf. Decision and Control, pp. 2661-2666, New Orleans, LA.

    Google Scholar 

  14. Brockett, R.W. (1993) Hybrid models for motion control systems. In: Trentel-man, H.L., and Willems, J.C. (eds) Essays in Control, pp. 29-53. Birkhäuser, Boston.

    Google Scholar 

  15. Cassandras, C.G., and Lafortune, S. (1999) Introduction to Discrete Event Systems. Kluwer Academic Publishers, Boston.

    MATH  Google Scholar 

  16. DeCarlo, R., Branicky, M.S., Pettersson, S., and Lennartson, B. (2000) Per-spectives and results on the stability and stabilizability of hybrid systems. Proc. IEEE, 88(2):1069-1082.

    Article  Google Scholar 

  17. Ghosh, R., and Tomlin, C. (2004) Symbolic reachable set computation of piece-wise affine hybrid automata and its application to biological modelling: Delta-Notch protein signalling. Systems Biology, 1(1):170-183.

    Article  Google Scholar 

  18. Gollu, A., and Varaiya, P.P. (1989) Hybrid dynamical systems. In: Proc. IEEE Conf. Decision and Control, pp. 2708-2712. Tampa, FL.

    Google Scholar 

  19. Grossman, R., Nerode, A., Ravn, A., and Rischel, H. (eds) (1993) Hybrid Systems. Springer, New York.

    Google Scholar 

  20. Harel, D. (1987) Statecharts: A visual formalism for complex systems. Science Computer Programming, 8:231-274.

    Article  MATH  MathSciNet  Google Scholar 

  21. Henzinger, T.A., Kopke, P.W., Puri, A., and Varaiya, P. (1998) What’s decid-able about hybrid automata? J. Computer and System Sciences, 57:94-124.

    Article  MATH  MathSciNet  Google Scholar 

  22. Hirsch, M.W., and Smale, S. (1974) Differential Equations, Dynamical Systems, and Linear Algebra. Academic Press, San Diego, CA.

    MATH  Google Scholar 

  23. Hopcroft, J.E., and Ullman, J.D. (1979) Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading, MA.

    MATH  Google Scholar 

  24. Liberzon, D. (2003) Switching in Systems and Control. Birkhauser, Boston.

    MATH  Google Scholar 

  25. Luenberger, D.G. (1979) Introduction to Dynamic Systems. Wiley, New York.

    MATH  Google Scholar 

  26. Maler, O., and Yovine, S. (1996) Hardware timing verification using KRONOS. In: Proc. 7th Israeli Conf. Computer Systems and Software Eng. Herzliya, Israel.

    Google Scholar 

  27. Meyer, G. (1994) Design of flight vehicle management systems. In: IEEE Conf. Decision and Control, Plenary Lecture. Lake Buena Vista, FL.

    Google Scholar 

  28. Nerode, A., and Kohn, W. (1993) Models for hybrid systems: Automata, topolo-gies, controllability, observability. In: Grossman, R., Nerode, A., Ravn, A., and Rischel, H. (eds) Hybrid Systems, pp. 317-356. Springer, New York.

    Google Scholar 

  29. Raibert, M.H. (1986) Legged Robots that Balance. MIT Press, Cambridge, MA.

    Google Scholar 

  30. Ramadge, P.J.G., and Wonham, M.W. (1989) The control of discrete event systems. Proc. IEEE, 77(1):81-98.

    Article  Google Scholar 

  31. Sontag, E.D. (1990) Mathematical Control Theory. Springer, New York.

    MATH  Google Scholar 

  32. Tabuada, P., Pappas, G.J., and Lima, P. (2001) Feasible formations of multi-agent systems. In: Proc. Amer. Control Conf., Arlington, VA.

    Google Scholar 

  33. Tavernini, L. (1987) Differential automata and their discrete simulators. Non-linear Analysis, Theory, Methods, and Applications, 11(6):665-683.

    Article  MATH  MathSciNet  Google Scholar 

  34. Tomlin, C., Lygeros, J., and Sastry, S. (2000) A game theoretic approach to controller design for hybrid systems. Proc. IEEE, 88(7):949-970.

    Article  Google Scholar 

  35. Tomlin, C., Pappas, G.J., and Sastry, S. (1998) Conflict resolution for air traffic management: A study in multi-agent hybrid systems. IEEE Trans. Automatic Control, 43(4):509-521.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  38. Zabczyk, J. (1973) Optimal control by means of switching. Studia Mathematica, 65:161-171.

    MathSciNet  Google Scholar 

  39. Zhang, J., Johansson, K.H., Lygeros, J., and Sastry, S. (2000) Dynamical sys-tems revisited: Hybrid systems with Zeno executions. In: Lynch, N., and Krogh,. B. (eds) Hybrid Systems: Computation and Control, pp. 451-464. Springer, Berlin.

    Chapter  Google Scholar 

  40. Zhang, W., Branicky, M.S., and Phillips, S.M. (2001) Stability of networked control systems. IEEE Control Systems Magazine, 21(1):84-99.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Birkhäuser Boston

About this chapter

Cite this chapter

Branicky, M.S. (2005). Introduction to Hybrid Systems. In: Hristu-Varsakelis, D., Levine, W.S. (eds) Handbook of Networked and Embedded Control Systems. Control Engineering. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4404-0_5

Download citation

  • DOI: https://doi.org/10.1007/0-8176-4404-0_5

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-3239-7

  • Online ISBN: 978-0-8176-4404-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics