Advertisement

Generalized linear complementarity problems and the analysis of continuously variable systems and discrete event systems

  • Bart De Schutter
  • Bart De Moor
Short Presentations
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1201)

Abstract

We present an overview of our research on the use of generalized linear complementarity problems (LCPs) for analysis of continuously variable systems and discrete event systems. We indicate how the Generalized LCP can be used to analyze piecewise-linear resistive electrical circuits. Next we discuss how the Extended LCP can be used to solve some fundamental problems that arise in max-algebraic system theory for discrete event systems. This shows that generalized LCPs appeax in the analysis and modeling of certain continuously variable systems and discrete event systems. Since hybrid systems exhibit characteristics of both continuously variable systems and discrete event systems, this leads to the question as to whether generalized LCPs can also play a role in the modeling and analysis of certain classes of hybrid systems.

Keywords

Hybrid System State Space Model Linear Complementarity Problem Discrete Event System Linear System Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    F. Baccelli, G. Cohen, G.J. Olsder, and J.P. Quadrat, Synchronization and Linearity. New York: John Wiley & Sons, 1992.Google Scholar
  2. 2.
    G. Cohen, D. Dubois, J.P. Quadrat, and M. Viot, “A linear-system-theoretic view of discrete-event processes and its use for performance evaluation in manufacturing,” IEEE Trans. on Aut. Control, vol. 30, no. 3, pp. 210–220, Mar. 1985.Google Scholar
  3. 3.
    R.W. Cottle, J.S. Pang, and R.E. Stone, The Linear Complementarity Problem. Boston: Academic Press, 1992.Google Scholar
  4. 4.
    B.De Moor, Mathematical Concepts and Techniques for Modelling of Static and Dynamic Systems. PhD thesis, Fac. of Applied Sc., K.U.Leuven, Belgium, 1988.Google Scholar
  5. 5.
    B.De Moor, L. Vandenberghe, and J. Vandewalle, “The generalized linear complementarity problem and an algorithm to find all its solutions,” Math. Prog., vol. 57, pp. 415–426, 1992.Google Scholar
  6. 6.
    B.De Schutter, Max-Algebraic System Theory for Discrete Event Systems. PhD thesis, Fac. of Applied Sc., K.U.Leuven, Belgium, 1996.Google Scholar
  7. 7.
    B.De Schutter and B.De Moor, “The extended linear complementarity problem,” Math. Prog., vol. 71, no. 3, pp. 289–325, Dec. 1995.Google Scholar
  8. 8.
    B.De Schutter and B.De Moor, “Minimal realization in the max algebra is an extended linear complementarity problem,” Syst. & Control Letters, vol. 25, no. 2, pp. 103–111, May 1995.Google Scholar
  9. 9.
    B. De Schutter and B. De Moor, “Applications of the extended linear complementarity problem in the max-plus algebra,” Proc. of WODES'96 (Internat. Workshop on Discrete Event Syst.), Edinburgh, UK, pp. 69–74, Aug. 1996.Google Scholar
  10. 10.
    B.De Schutter and B.De Moor, “A method to find all solutions of a system of multivariate polynomial equalities and inequalities in the max algebra,” Discrete Event Dynamic Systems: Theory and Appl., vol. 6, no. 2, pp. 115–138, Mar. 1996.Google Scholar
  11. 11.
    B.De Schutter and B.De Moor, “Optimal traffic signal control for a single intersection,” Tech. rep. 96-90, ESAT/SISTA, K.U.Leuven, Belgium, Dec. 1996.Google Scholar
  12. 12.
    J.M. Schumacher, “Some modeling aspects of unilaterally constrained dynamics,” Proc. of the ESA Internat. Workshop on Adv. Math. Methods in the Dynamics of Flexible Bodies, Noordwijk, The Netherlands, June 1996.Google Scholar
  13. 13.
    L. Vandenberghe, B.De Moor, and J. Vandewalle, “The generalized linear complementarity problem applied to the complete analysis of resistive piecewise-linear circuits,” IEEE Trans. on Circ. and Syst., vol. 36, no. 11, pp. 1382–1391, Nov. 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Bart De Schutter
    • 1
  • Bart De Moor
    • 1
  1. 1.ESAT/SISTAK.U.LeuvenLeuvenBelgium

Personalised recommendations