Approximate bisimulations for constrained linear systems

Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

Volumn 2005, Issue , 2005, Pages 4700-4705

  Girard, Antoine ^a   Pappas, George J ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BISIMULATION EQUIVALENCE; BOUNDED DISTURBANCES; CONTINUOUS-TIME SYSTEMS; NONDETERMINISTIC EVOLUTION; TRANSITION SYSTEMS;

APPROXIMATION THEORY; COMPUTER SIMULATION; DISCRETE TIME CONTROL SYSTEMS; FUNCTION EVALUATION; GAME THEORY; LYAPUNOV METHODS;

LINEAR CONTROL SYSTEMS;

EID: 33847242933     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2005.1582904     Document Type: Conference Paper

References (20)

1. A. C. Antoulas, D. C. Sorensen, and S. Gugercin. "A survey of model reduction methods for large-scale systems," Contemporary Mathematics, vol. 280, pp. 193-219, 2000.
2. C. L. Beck, J. Doyle, and K. Glover, "Model reduction of multi-dimensional and uncertain systems," IEEE Transactions on Automatic Control, vol. 41, no. 10, pp. 1466-1477, October 1996.
3. E. M. Clarke, O. Grumberg, and D. A. Peled, Model Checking. MIT Press, 2000.
4. L. de Alfaro, M. Faella, and M. Stoelinga, "Linear and branching metrics for quantitative transition systems." in ICALP'04, ser. LNCS. Springer, 2004, vol. 3142, pp. 1150-1162.
5. J. Desharnais, V. Gupta, R. Jagadeesan, and P. Panangaden, "Metrics for labelled markov processes," Theoretical Computer Science, vol. 318, no. 3, pp. 323-354, June 2004.
6. R. A. Freeman and P. V. Kokotovic, "Inverse optimality in robust stabilization," SIAM J. Control and Optimization, vol. 34, no. 4, pp. 1365-1391, July 1996.
7. A. Girard, "Reachability of uncertain linear systems using zonotopes," in Hybrid Systems: Computation and Control, ser. LNCS. Springer, 2005, vol. 3414, pp. 291-305.
8. A. Girard and G. J. Pappas, "Approximate bisimulations for nonlinear systems," in Proc. 44th IEEE Conference on Decision and Control and European Control Conference, December 2005.
9. _, "Approximation metrics for discrete and continuous systems," May 2005, technical Report MS-CIS-05-10, Dept. of CIS. University of Pennsylvania.
10. E. Haghverdi, P. Tabuada, and G. J. Pappas, "Bisimulation relations for dynamical, control, and hybrid systems," Theoretical Computer Science, vol. 342, pp. 229-261, 2005.
11. Z. Han and B. H. Krogh, "Reachability of hybrid control systems using reduced-order models," in Proc. American Control Conference, Boston, MA, July 2004.
12. B. H. Krogh and O. Stursberg, "On efficient representation and computation of reachable sets for hybrid systems," in Hybrid Systems: Computation and Control, ser. LNCS. Springer, 2003, vol. 2623, pp. 482-497.
13. D. Liberzon, E. D. Sontag, and Y. Wang, "Universal construction of feedback laws achieving ISS and integral-ISS disturbance attenuation," Systems and Control Letters, vol. 46, pp. 111-127, 2002.
14. G. J. Pappas, "Bisimilar linear systems," Automatica. vol. 39, no. 12, pp. 2035-2047, December 2003.
15. J. F. Sturm, "Using SEDUMI 1.02, a MATLAB toolbox for optimization over symmetric cones," Optimization Methods and Softwares, vol. 11-12, pp. 625-653, 1999.
16. H. Tanner and G. J. Pappas, "Abstractions of constrained linear systems," in Proc. American Control Conference, Denver, CO, June 2003.
17. K. C. Toh, R. H. Tutuncu, and M. J. Todd. SDPT3 - a MATLAB software package for semidefinite quadratic linear programming. [Online]. Available: http://www.math.nus.edu.sg/~mattohkc/sdpt3.html
18. F. van Breugel, M. Mislove, J. Ouaknine, and J. Worrell, "An intrinsic characterization of approximate probabilistic bisimilarity," in Foundations of Software Science and Computation Structures, ser. LNCS. Springer, 2003, vol. 2620, pp. 200-215.
19. A. van der Schaft, "Equivalence of dynamical systems by bisimulation," IEEE Trans. Automatic Control, vol. 49, pp. 2160-2172, 2004.
20. H. Yazarel and G. J. Pappas, "Geometric programming relaxations for linear system reachability," in Proc. American Control Conference, Boston, MA, June 2004.