An equivalence between a control network and a switched hybrid system

  • Linda Bushnell
  • Octavian Beldiman
  • Gregory Walsh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1386)


A simple model for ideal control networks is proposed in this paper. A model for hybrid systems due to Witsenhausen is extended by adding both a discrete output and input. This extended model is used for modeling an ideal network of interactive hybrid systems. An equivalence is established between the network model and the Witsenhausen model. This equivalence allows for simulating complicated systems, and extending different properties of Witsenhausen type systems to control network systems. A simple HVAC application is modeled using the above equivalence.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. S. Witsenhausen. “A class of hybrid-state continuous time dynamic systems,” IEEE Transactions on Automatic Control, 11(2):161–167, v1966.Google Scholar
  2. 2.
    R. S. Raji. “Smart networks for control,” IEEE Spectrum, June 1994, p. 49–55.Google Scholar
  3. 3.
    D. Radford. “Spread-spectrum data leap through ac power wiring,” IEEE Spectrum, November 1996, p. 48–53.Google Scholar
  4. 4.
    G. Walsh. “On race conditions for networked control systems,” in Proceedings of the 30th CISS,Princeton, NJ, March 1996, p 411–415.Google Scholar
  5. 5.
    K. Tindell, A. Burns and A.J. Wellings. “Calculating controller area network (CAN) message response times,” Control Eng. Practice, vol. 3, no. 8, p. 1168–1169, 1995.Google Scholar
  6. 6.
    M. S. Branicky. “Studies in hybrid systems: modeling, analysis, and control,” Ph.D. dissertation, MIT, June 1995.Google Scholar
  7. 7.
    A. Back, J. Guckenheimer and M. Myers. “A dynamical simulation facility for hybrid systems,” in R. L. Grossman, A. Nerode, A. P. Ravn, H. Rischel et al. Hybrid Systems p. 255–267. Springer-Verlag, New York, 1993.Google Scholar
  8. 8.
    A. Nerode and W. Kohn. “Models for hybrid systems: Automata, topologies stability.“ In R. L. Grossman, A. Nerode, A. P. Ravn, H. Rischel et al. Hybrid Systems et al., p. 317–356. Springer-Verlag, New York, 1993.Google Scholar
  9. 9.
    L. Tavernini. “Differential automata and their discrete simulators.“ in Nonlinear analysis, Theory, Methods and Applications, 11(6): 665–683, 1987.Google Scholar
  10. 10.
    W. S. Wong and R. W. Brockett. “Systems with finite communication bandwidth constraints — Part I: State estimation problems,” in IEEE Transactions on Automatic Control, 42(9): 1294–1299.Google Scholar
  11. 11.
    R. 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, p. 29–53, 1993.Google Scholar
  12. 12.
    R. W. Brockett. “Dynamical systems and their associated automata.“ in U.Helmke, R. Menniken and J.Saurer, editors, Systems and networks: Mathematical theory and applications. Akademie Verlag, Berlin 1994.Google Scholar
  13. 13.
    R. L. Grossman, A. Nerode, A. P. Ravn, H. Rischel editors Hybrid systems, volume 736 of Lecture notes in computer science. Springer-Verlag, New York, 1993.Google Scholar
  14. 14.
    U. Özgüner, H. Goktas, H. Chan. Automotive suspension control through a computer communication network. Vt IEEE Conference on Control Application, 1992.Google Scholar
  15. 15.
    J. Bräuninger, R. Emig, T. Küttner and A. Löfffe.Controller Area Network for Truck and Bus Application., SAE Transactions, v 99, sect 2, 1990, p 704–714.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Linda Bushnell
    • 1
  • Octavian Beldiman
    • 2
  • Gregory Walsh
    • 3
  1. 1.U.S. Army Research OfficeRTPUSA
  2. 2.Department of Electrical and Computer EngineeringDuke UniversityDurhamUSA
  3. 3.Department of Mechanical EngineeringUniversity of MarylandCollege Park

Personalised recommendations