Approximate bisimulation for a class of stochastic hybrid systems

Proceedings of the American Control Conference

Volumn 2006, Issue , 2006, Pages 4724-4729

  Julius, A Agung ^a   Girard, Antoine ^a   Pappas, George J ^b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b VERIMAG   (France)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; FUNCTION EVALUATION; STOCHASTIC CONTROL SYSTEMS;

JUMP LINEAR STOCHASTIC SYSTEMS (JLSS); QUADRATIC STOCHASTIC BISIMULATION FUNCTIONS; SAFETY VERIFICATION; TRACTABLE LINEAR MATRIX INEQUALITY PROBLEM;

COMPUTER SIMULATION;

EID: 34047221350     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/acc.2006.1657467     Document Type: Conference Paper

References (30)

1. A. Abate, L. Shi, S. Simic, and S. Sastry. A stability criterion for stochastic hybrid systems. In Proc. of Mathematical Theory of Networks and Systems, Leuven, July 2004.
2. A. Bemporad and S. Di Cairano. Optimal control of discrete hybrid stochastic automata. In Morari and Thiele [20], pages 151-167.
3. M. L. Bujorianu, J. Lygeros, and M. C. Bujorianu. Bisimulation for general stochastic hybrid systems. In Morari and Thiele [20], pages 198-214.
4. 2-control of markovian jump linear systems via convex analysis. Automatica, 35(2):259-268, 1999.
5. M. H. A. Davis. Markov models and optimization. Chapman and Hall, London, 1993.
6. L. de Alfaro, M. Faella, and M. Stoelinga. Linear and branching system metrics. UCSC-CRL-05-01, School of Engineering, University of California at Santa Cruz, 2005.
7. J. Desharnais, A. Edalat, and P. Panangaden. Bisimulation for labelled Markov processes. Information and Computation, 179(2): 163-193, 2002.
8. J. Desharnais, V. Gupta, R. Jagadeesan, and P Panangaden. Metrics for labelled Markov processes. Theoretical Computer Science, 318(3):323-354, 2004.
9. P Florchinger. Lyapunov-like techniques for stochastic stability. SIAM Journal on Control and Optimization, 33:1151-1169, 1995.
10. M. K. Ghosh, A. Arapostathis, and S. Marcus. Ergodic control of switching diffusions. SIAM Journal on Control and Optimization, 35(6): 1952-1988, 1997.
11. A. Girard and G. J. Pappas. Approximate bisimulation for constrained linear systems. In Proc. of the IEEE Conf. Decision and Control, Seville, Spain, 2005.
12. A. Girard and G. J. Pappas. Approximation metrics for discrete and continuous systems. MS-CIS-05-10, Dept. Computer and Information Science, University of Pennsylvania, Philadelphia, USA, May 2005.
13. J. P. Hespanha. Stochastic hybrid systems: applications to communication networks. In R. Alur and G. J. Pappas, editors, HSCC, volume 2993 of Lecture Notes in Computer Science, pages 387-401. Springer Verlag, 2004.
14. J. P. Hespanha. Polynomial stochastic hybrid systems. In Morari and Thiele [20], pages 322-338.
15. J. Hu, J. Lygeros, and S. Sastry. Towards a theory of stochastic hybrid systems. In N. Lynch and B. H. Krogh, editors, Hybrid Systems: Computation and Control, volume 1790 of Lecture Notes in Computer Science, pages 160-173. Springer Verlag, 2000.
16. X. D. Koutsoukos. Optimal control of stochastic hybrid systems based on locally consistent Markov decision processes. International Journal of Hybrid Systems, 4:301-318, 2004.
17. J. Löfberg. http://control.ee.ethz.ch/~joloef/yalmip.php.
18. N. Lopez and M. Núñez. An overview of probabilistic process algebras and their equivalences. In C. Baier, B. R. Haverkort, and H. Hermanns, editors, Validation of Stochastic Systems: A Guide to Current Research, volume 2925 of Lecture Notes in Computer Science, pages 89-123. Springer, 2004.
19. R. Milner. Communication and concurrency. Prentice Hall International, 1989.
20. M. Morari and L. Thiele, editors. Hybrid systems: computation and control, volume 3414 of Lecture Notes in Computer Science. Springer Verlag, 2005.
21. B. Oksendal. Stochastic differential equations: an introduction with applications. Springer-Verlag, Berlin, 2000.
22. G. J. Pappas. Bisimilar linear systems. Automatica, 39:2035-2047, December 2003.
23. G. Pola, M. Bujorianu, J. Lygeros, and M. D. Benedetto. Stochastic hybrid models: an overview. In Proc. IFAC Conf. Analysis and Design of Hybrid Systems, St. Malo, 2003. IFAC.
24. S. Strubbe and A. J. van der Schaft. Bisimulation for communicating piecewise deterministic Markov processes. In Morari and Thiele [20], pages 623-639.
25. S. N. Strubbe, A. A. Julius, and A. J. van der Schaft. Communicating piecewise deterministic Markov processes. In Proc. IFAC Conf. Analysis and Design of Hybrid Systems, pages 349-354, St. Malo, 2003. IFAC.
26. P. Tabuada, G. J. Pappas, and P. Lima. Compositional abstractions of hybrid control systems. Discrete event dynamic systems, 14(2):203-238, April 2005.
27. A. J. van der Schaft. Equivalence of dynamical systems by bisimulation. IEEE Trans. Automatic Control, 49(12):2160-2172, December 2004.
28. R. Vidal, A. Chiuso, and S. Soatto. Observability and idetifiability of jump linear systems. In Proceedings 41st IEEE Conf. Decision and Control, pages 3614-3619, Las Vegas, 2002. IEEE.
29. M. Ying and M. Wirsing. Approximate bisimilarity. In T. Rus, editor, AMAST 2000, volume 1816 of Lecture Notes in Computer Science, pages 309-322. Springer Verlag, 2000.
30. ∞ model reduction of markovian jump linear systems. Systems and control letters, 50:103-118, 2003.