The extended linear complementarity problem and the modeling and analysis of hybrid systems

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1567, Issue , 1999, Pages 70-85

  Schutter, Bart De ^a   Moor, Bart De ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

DISCRETE EVENT SIMULATION;

CONTINUOUS VARIABLE SYSTEM; CONTINUOUS VARIABLES; FUNCTION OF TIME; LINEAR COMPLEMENTARITY PROBLEMS; MATHEMATICAL PROGRAM; MODEL AND ANALYSIS; QUEUE LENGTHS;

HYBRID SYSTEMS;

EID: 0013250170     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: None     Document Type: Conference Paper

References (23)

1. F. Baccelli, G. Cohen, G. J. Olsder, and J. P. Quadrat, Synchronization and Linearity. New York: John Wiley & Sons, 1992.
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 manufactur-ing, " IEEE Transactions on Automatic Control, vol. 30, no. 3, pp. 210-220, Mar. 1985.
3. R. W. Cottle, J. S. Pang, and R. E. Stone, The Linear Complementarity Problem. Boston: Academic Press, 1992.
4. R. A. Cuninghame-Green, Minimax Algebra, vol. 166 of Lecture Notes in Economics and Mathematical Systems. Berlin, Germany: Springer-Verlag, 1979.
5. B. De Moor, Mathematical Concepts and Techniques for Modelling of Static and Dynamic Systems. PhD thesis, Faculty of Applied Sciences, K. U. Leuven, Leuven, Belgium, June 1988.
6. B. De Schutter, Max-Algebraic System Theory for Discrete Event Systems. PhD thesis, Faculty of Applied Sciences, K. U. Leuven, Leuven, Belgium, Feb. 1996.
7. B. De Schutter and B. De Moor, “The extended linear complementarity problem, " Mathematical Programming, vol. 71, no. 3, pp. 289-325, Dec. 1995.
8. B. De Schutter and B. De Moor, “Minimal realization in the max algebra is an extended linear complementarity problem, " Systems & Control Letters, vol. 25, no. 2, pp. 103-111, May 1995.
9. B. De Schutter and B. De Moor, “Applications of the extended linear comple-mentarity problem in the max-plus algebra, " in Proceedings of the International Workshop on Discrete Event Systems (WODES'96), Edinburgh, UK, pp. 69-74, Aug. 1996.
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 Applications, vol. 6, no. 2, pp. 115-138, Mar. 1996.
11. B. De Schutter and B. De Moor, “The Linear Dynamic Complementarity Prob-lem is a special case of the Extended Linear Complementarity Problem, " Tech. rep. 97-21, ESAT-SISTA, K. U. Leuven, Leuven, Belgium, Mar. 1997. Accepted for publication in Systems & Control Letters, vol. 34, no. 1-2, pp. 63-75, June 1998.
12. B. De Schutter and B. De Moor, “Optimal trafic light control for a single intersec-tion, " Tech. rep. 96-90, ESAT-SISTA, K. U. Leuven, Leuven, Belgium, Jan. 1998. Revised version. Accepted for publication in European Journal of Control.
13. B. De Schutter and B. De Moor, “Optimal trafic light control for a single intersec-tion: Addendum, " Tech. rep. 96-90a, ESAT-SISTA, K. U. Leuven, Leuven, Belgium, Jan. 1998.
14. N. H. Gartner, J. D. C. Little, and H. Gabbay, “Simultaneous optimization of offisets, splits, and cycle time, " Transportation Research Record, vol. 596, pp. 6-15, 1976.
15. S. Gaubert, Théorie des Systémes Linéaires dans les Dioïdes. PhD thesis, Ecole Nationale Supérieure des Mines de Paris, France, July 1992.
16. J. H. Lim, S. H. Hwang, I. H. Suh, and Z. Bien, “Hierarchical optimal control of oversaturated urban trafic networks, " International Journal of Control, vol. 33, no. 4, pp. 727-737, Apr. 1981.
17. D. Lin, F. Ulrich, L. L. Kinney, and K. S. P. Kumar, “Hierarchical techniques in trafic control, " in Proceedings of the IFAC/IFIP/IFORS 3rd International Symposium, pp. 163-171, 1976.
18. E. S. Park, J. H. Lim, I. H. Suh, and Z. Bien, “Hierarchical optimal control of urban trafic networks, " International Journal of Control, vol. 40, no. 4, pp. 813-829, Oct. 1984.
19. J. M. Schumacher, “Some modeling aspects of unilaterally constrained dynamic-s, " in Proceedings of the ESA International Workshop on Advanced Mathematical Methods in the Dynamics of Flexible Bodies, ESA-ESTEC, Noordwijk, The Nether-lands, June 1996.
20. M. G. Singh and H. Tamura, “Modelling and hierarchical optimization for over-saturated urban road trafic networks, " International Journal of Control, vol. 20, no. 6, pp. 913-934, 1974.
21. A. J. van der Schaft and J. M. Schumacher, “Hybrid systems described by the com-plementarity formalism, " in Proceedings of the International Workshop on Hybrid and Real-Time Systems (HART'97), Grenoble, France, vol. 1201 of Lecture Notes in Computer Science, pp. 403-408, Springer-Verlag, 1997.
22. A. J. van der Schaft and J. M. Schumacher, “Complementarity modeling of hybrid systems, " IEEE Transactions on Automatic Control, vol. 43, no. 4, pp. 483-490, Apr. 1998.
23. L. Vandenberghe, B. De Moor, and J. Vandewalle, “The generalized linear com-plementarity problem applied to the complete analysis of resistive piecewise-linear circuits, " IEEE Transactions on Circuits and Systems, vol. 36, no. 11, pp. 1382-1391, Nov. 1989.