A stochastic games framework for verification and control of discrete time stochastic hybrid systems

Automatica

Volumn 49, Issue 9, 2013, Pages 2665-2674

  Ding, Jerry ^a,b   Kamgarpour, Maryam ^b   Summers, Sean ^b   Abate, Alessandro ^c   Lygeros, John ^b   Tomlin, Claire ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b ETH ZURICH   (Switzerland)

^c UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Controller synthesis; Dynamic games; Hybrid systems; Reachability; Stochastic systems

Indexed keywords

AIR TRAFFIC MANAGEMENT; CONTROLLER SYNTHESIS; DISTURBANCE STRATEGIES; DYNAMIC GAME; REACHABILITY; STOCHASTIC HYBRID SYSTEMS; SYNTHESIS OF OPTIMAL CONTROL; ZERO-SUM STOCHASTIC GAMES;

ALGORITHMS; GAME THEORY; HYBRID SYSTEMS; STOCHASTIC SYSTEMS;

STOCHASTIC CONTROL SYSTEMS;

EID: 84881481163     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2013.05.025     Document Type: Conference Paper

References (45)

1. Abate, A., Amin, S., Prandini, M., Lygeros, J., & Sastry, S. (2006). Probabilistic reachability and safe sets computation for discrete time stochastic hybrid systems. In Proceedings of the 45th IEEE conference on decision and control (pp. 258-263). December.
2. A. Abate, J.P. Katoen, J. Lygeros, and M. Prandini Approximate model checking of stochastic hybrid systems European Journal of Control 16 6 2010 624 641
3. A. Abate, M. Prandini, J. Lygeros, and S. Sastry Probabilistic reachability and safety for controlled discrete time stochastic hybrid systems Automatica 44 11 2008 2724 2734
4. A. Ames, R. Sinnet, and E. Wendel Three-dimensional kneed bipedal walking: a hybrid geometric approach R. Majumdar, P. Tabuada, Hybrid systems: computation and control Lecture notes in computer science vol. 5469 2009 Springer 16 30
5. S. Amin, A. Cardenas, and S. Sastry Safe and secure networked control systems under denial-of-service attacks R. Majumdar, P. Tabuada, Hybrid systems: computation and control Lecture notes in computer science vol. 5469 2009 Springer 31 45
6. A. Balluchi, L. Benvenuti, M. Di Benedetto, C. Pinello, and A. Sangiovanni-Vincentelli Automotive engine control and hybrid systems: challenges and opportunities Proceedings of the IEEE 88 7 2000 888 912
7. Bect, J., Phulpin, Y., Baili, H., & Fleury, G. (2006). On the Fokker-Planck equation for stochastic hybrid systems: application to a wind turbine model. In International conference on probabilistic methods applied to power systems (pp. 1-6).
8. A. Bensoussan, and J. Menaldi Stochastic hybrid control Journal of Mathematical Analysis and Applications 249 1 2000 261 288
9. D.P. Bertsekas, and S.E. Shreve Stochastic optimal control: the discrete time case 1978 Academic Press New York, NY
10. D.P. Bertsekas, and J. Tsitsiklis Neuro-dynamic programming 1996 Athena Scientific Belmont, MA
11. M. Breton, A. Alj, and A. Haurie Sequential Stackelberg equilibria in two-person games Journal of Optimization Theory and Applications 59 1 1988 71 97
12. L.D. Brown, and R. Purves Measurable selections of extrema The Annals of Statistics 1 5 1973 902 912
13. M. Bujorianu Extended stochastic hybrid systems and their reachability problem R. Alur, G. Pappas, Hybrid systems: computation and control Lecture notes in computer science vol. 2993 2004 Springer 234 249
14. Esmaeil Zadeh Soudjani, S., & Abate, A. (2011). Adaptive gridding for abstraction and verification of stochastic hybrid systems. In Proceedings of the 8th international conference on quantitative evaluation of systems.
15. G.B. Folland Real analysis: modern techniques and their applications 1999 John Wiley & Sons New York, NY
16. R. Ghosh, and C. Tomlin Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modelling: Delta-Notch protein signalling Systems Biology 1 1 2004 170 183
17. W. Glover, and J. Lygeros A stochastic hybrid model for air traffic control simulation R. Alur, G.J. Pappas, Hybrid systems: computation and control Lecture notes in computer science vol. 2993 2004 Springer 372 386
18. J.I. Gonzalez-Trejo, O. Hernandez-Lerma, and L.F. Hoyos-Reyes Minimax control of discrete-time stochastic systems SIAM Journal on Control and Optimization 41 5 2002 1626 1659
19. H. Hansson, and B. Jonsson A logic for reasoning about time and reliability Formal Aspects of Computing 6 1994 512 535
20. J.P. Hespanha Stochastic hybrid systems: application to communication networks R. Alur, G.J. Pappas, Hybrid systems: computation and control Lecture notes in computer science vol. 2993 2004 Springer 47 56
21. J. Hu, J. Lygeros, and S. Sastry Towards a theory of stochastic hybrid systems N. Lynch, B. Krogh, Hybrid systems: computation and control Lecture notes in computer science vol. 1790 2000 Springer 160 173
22. J. Hu, M. Prandini, and S. Sastry Aircraft conflict prediction in the presence of a spatially correlated wind field IEEE Transactions on Intelligent Transportation Systems 6 3 2005 326 340
23. I. Hwang, and C.E. Seah Intent-based probabilistic conflict detection for the next generation air transportation system Proceedings of the IEEE 96 12 2008 2040 2059
24. Kamgarpour, M., Ding, J., Summers, S., Abate, A., Lygeros, J., & Tomlin, C. (2011). Discrete time stochastic hybrid dynamic games: verification & controller synthesis. In Proceedings of the 50th IEEE conference on decision and control (pp. 6122-6127). December.
25. X. Koutsoukos, and D. Riley Computational methods for reachability analysis of stochastic hybrid systems J.P. Hespanha, A. Tiwari, Hybrid systems: computation and control Lecture notes in computer science vol. 3927 2006 Springer 377 391
26. J.K. Kuchar, and L.C. Yang A review of conflict detection and resolution modeling methods IEEE Transactions on Intelligent Transportation Systems 1 4 2000 179 189
27. P.R. Kumar, and T.H. Shiau Existence of value and randomized strategies in zero-sum discrete-time stochastic dynamic games SIAM Journal on Control and Optimization 19 5 1981 617 634
28. H.J. Kushner, and P. Dupuis Numerical methods for stochastic control problems in continuous time 1992 Springer-Verlag London, UK
29. P. Lincoln, and A. Tiwari Symbolic systems biology: hybrid modeling and analysis of biological networks R. Alur, G. Pappas, Hybrid systems: computation and control Lecture notes in computer science vol. 2993 2004 Springer 147 165
30. J. Lygeros, C. Tomlin, and S. Sastry Controllers for reachability specifications for hybrid systems Automatica 35 3 1999 349 370
31. A. Maitra, and T. Parthasarathy On stochastic games Journal of Optimization Theory and Applications 5 4 1970 289 300
32. A. Maitra, and W. Sudderth Finitely additive stochastic games with Borel measurable payoffs International Journal of Game Theory 27 2 1998 257 267
33. Mohajerin Esfahani, P., Chatterjee, D., & Lygeros, J. (2011). On a problem of stochastic reach-avoid set characterization. In Proceedings of the 50th IEEE conference on decision and control (pp. 7069-7074). December.
34. A.S. Nowak Universally measurable strategies in zero-sum stochastic games The Annals of Probability 13 1 1985 269 287
35. R.A. Paielli, and H. Erzberger Conflict probability estimation for free flight AIAA Journal of Guidance, Control and Dynamics 20 3 1997 588 596
36. S. Prajna, A. Jadbabaie, and G. Pappas A framework for worst-case and stochastic safety verification using barrier certificates IEEE Transactions on Automatic Control 52 8 2007 1415 1428
37. M. Prandini, J. Hu, J. Lygeros, and S. Sastry A probabilistic approach to aircraft conflict detection IEEE Transactions on Intelligent Transportation Systems 1 4 2000 199 220
38. U. Rieder Non-cooperative dynamic games with general utility functions T.E.S. Raghavan, T.S. Ferguson, T. Parthasarathy, O.J. Vrieze, Stochastic games and related topics 1991 Kluwer Academic Publishers 161 174
39. W. Rudin Principles of mathematical analysis 3rd ed. 1976 McGraw-Hill New York, NY
40. Sastry, S., Meyer, G., Tomlin, C., Lygeros, J., Godbole, D., & Pappas, G. (1995). Hybrid control in air traffic management systems. In Proceedings of the 34th IEEE conference on decision and control, vol. 2 (pp. 1478-1483).
41. L.S. Shapley Stochastic games Proceedings of the National Academy of Sciences 39 10 1953 1095 1100
42. S. Summers, M. Kamgarpour, J. Lygeros, and C. Tomlin A stochastic reach-avoid problem with random obstacles Proceedings of the 14th international conference on hybrid systems: computation and control 2011 ACM 251 260
43. S. Summers, and J. Lygeros Verification of discrete time stochastic hybrid systems: a stochastic reach-avoid decision problem Automatica 46 12 2010 1951 1961
44. C. Tomlin, G. Pappas, and S. Sastry Conflict resolution for air traffic management: a study in multiagent hybrid systems IEEE Transactions on Automatic Control 43 4 2002 509 521
45. L.C. Yang, and L. Kuchar Prototype conflict alerting system for free flight AIAA Journal of Guidance, Control and Dynamics 20 4 1997 768 773