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Efficient Mode Enumeration of Compositional Hybrid Systems

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Hybrid Systems: Computation and Control (HSCC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2623))

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Abstract

A hyperplane arrangement is a polyhedral cell complex where the relative position of each cell of the arrangement and the composing hyperplanes are summarized by a sign vector computable in polynomial time. This tool from computational geometry enables the development of a fast and efficient algorithm that translates the composition of hybrid systems into a piecewise affine model. The tool provides also information on the real combinatorial degree of the system which can be used to reduce the size of the search tree and the computation time of the optimization algorithms underlying optimal and model predictive control.

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References

  1. R. Alur, T. Dang, J. Esposito, R. Fierro, Y. Hur, F. Ivančić, V. Kumar, I. Lee, P. Mishra, G. Pappas, and O. Sokolsky. Hierarchical hybrid modeling of embedded systems. Volume 2211 of Lecture Notes in Computer Science, pages 14–31. Springer Verlag, 2001.

    Google Scholar 

  2. R. Alur and T. A. Henzinger. Modularity for timed and hybrid systems. Volume 1243 of Lecture Notes in Computer Science, pages 74–88, Springer Verlag, 1997.

    Google Scholar 

  3. D. Avis and K. Fukuda. Reverse search for enumeration. Discrete Applied Mathematics, 65:21–46, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Bemporad. An efficient technique for translating mixed logical dynamical systems into piecewise affine systems. In Proc. 41st IEEE Conf. on Decision and Control, 2002.

    Google Scholar 

  5. A. Bemporad, N. Giorgetti, I. V. Kolmanovsky, and D. Hrovat. A hybrid systems approach to modeling and optimal control of disc engines. In Proc. 41st IEEE Conf. on Decision and Control, 2002.

    Google Scholar 

  6. A. Bemporad and D. Mignone. MIQP.M: A Matlab function for solving mixed integer quadratic programs. ETH Zurich, 2000.

    Google Scholar 

  7. A. Bemporad and M. Morari. Control of systems integrating logic, dynamics, and constraints. Automatica, 35(3):407–427, March 1999.

    Article  MATH  MathSciNet  Google Scholar 

  8. F. Borrelli, A. Bemporad, M. Fodor, and D. Hrovat. A hybrid approach to traction control. Volume 2034 of Lecture Notes in Computer Science, pages 162–174. Springer Verlag, 2001.

    Google Scholar 

  9. R. C. Buck. Partition of space. Amer. Math. Monthly, 50:541–544, 1943.

    Article  MATH  MathSciNet  Google Scholar 

  10. B. De Schutter and T. van den Boom. On model predictive control for max-minplus-scaling discrete event systems. Automatica, 37(7):1049–1056, 2001.

    Article  MATH  Google Scholar 

  11. N. Deo. Graph Theory with Applications to Engineering and Computer Science. Prentice-Hall, Inc., 1974.

    Google Scholar 

  12. P. Eades, X. Lin, and W. F. Smyth. A fast and effective heuristic for the feedback arc set problem. Information Processing Letters, 47:319–323, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  13. M. G. Earl and R. D’Andrea. Modeling and control of a multi-vehicle system using mixed integer linear programming. In Proc. 41st IEEE Conf. on Decision and Control, 2002.

    Google Scholar 

  14. H. Edelsbrunner. Algorithms in Combinatorial Geometry. 1987.

    Google Scholar 

  15. J. A. Ferrez and K. Fukuda. Implementations of LP-based reverse search algorithms for the zonotope construction and the fixed-rank convex quadratic maximization in binary variables using the ZRAM and the cddlib libraries. Technical report, July 2002. http://www.cs.mcgill.ca/~fukuda/download/mink.

  16. J. A. Ferrez, K. Fukuda, and Th. M. Liebling. Cuts, zonotopes and arrangements. Technical report, EPF Lausanne, November 2001.

    Google Scholar 

  17. T. Geyer, F. D. Torrisi, and M. Morari. Efficient Mode Enumeration of Compositional Hybrid Systems. Technical Report AUT03-01, ETH Zurich, 2003.

    Google Scholar 

  18. W. P. M. H. Heemels, B. De Schutter, and A. Bemporad. Equivalence of hybrid dynamical models. Automatica, 37(7):1085–1091, July 2001.

    Article  MATH  Google Scholar 

  19. T. A. Henzinger, M. Minea, and V. Prabhu. Assume-guarantee reasoning for hierarchical hybrid systems. Volume 2034 of Lecture Notes in Computer Science, pages 275–290. Springer Verlag, March 2001.

    Google Scholar 

  20. ILOG, Inc. CPLEX 8.0 User Manual. Gentilly Cedex, France, 2002.

    Google Scholar 

  21. K. H. Johansson. Hybrid systems:modeling, analysis and control-composition of hybrid automata. Lecture notes of the class EECS 291e, Lecture 5, University of California at Berkley, 2000.

    Google Scholar 

  22. N. Lynch, R. Segala, and F. Vaandrager. Hybrid I/O automata revisited. Volume 2034 of Lecture Notes in Computer Science, pages 403–417. Springer Verlag, 2001.

    Google Scholar 

  23. D. Mignone. Control and Estimation of Hybrid Systems with Mathematical Optimization. Diss. ETH No. 14520, ETH Zurich, 2002.

    Google Scholar 

  24. S. Rashid and J. Lygeros. Hybrid systems:modeling, analysis and control-open hybrid automata and composition. Lecture notes of the class EECS 291e, Lecture 8, University of California at Berkley, 1999.

    Google Scholar 

  25. E. D. Sontag. Nonlinear regulation: The piecewise linear approach. IEEE Trans. on Aut. Control, 26(2):346–358, April 1981.

    Article  MATH  MathSciNet  Google Scholar 

  26. E. D. Sontag. Interconnected automata and linear systems: A theoretical framework in discrete-time. Volume 1066 of Lecture Notes in Computer Science, pages 436–448. Springer-Verlag, 1996.

    Google Scholar 

  27. F. D. Torrisi and A. Bemporad. Discrete-time hybrid modeling and verification. In Proc. 40th IEEE Conf. on Decision and Control, pages 2899–2904, 2001.

    Google Scholar 

  28. F. D. Torrisi and A. Bemporad. Hysdel — a tool for generating computational hybrid models for analysis and synthesis problems. Technical Report AUT02-03, ETH Zurich, http://control.ethz.ch/~hybrid/hysdel, March 2002.

  29. A. J. van der Schaft and J. M. Schumacher. Complementarity modelling of hybrid systems. IEEE Trans. on Aut. Control, 43:483–490, 1998.

    Article  MATH  Google Scholar 

  30. G. M. Ziegler. Lectures on Polytopes, volume 152 of Graduate Texts in Mathematics. Springer, New York, 1994.

    Google Scholar 

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Geyer, T., Torrisi, F.D., Morari, M. (2003). Efficient Mode Enumeration of Compositional Hybrid Systems. In: Maler, O., Pnueli, A. (eds) Hybrid Systems: Computation and Control. HSCC 2003. Lecture Notes in Computer Science, vol 2623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36580-X_18

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  • DOI: https://doi.org/10.1007/3-540-36580-X_18

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  • Print ISBN: 978-3-540-00913-9

  • Online ISBN: 978-3-540-36580-8

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