Probabilistic reachability and safety for controlled discrete time stochastic hybrid systems

Automatica

Volumn 44, Issue 11, 2008, Pages 2724-2734

  Abate, Alessandro ^a   Prandini, Maria ^b   Lygeros, John ^c   Sastry, Shankar ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b POLITECNICO DI MILANO   (Italy)

^c ETH ZURICH   (Switzerland)

Author keywords

Dynamic programming; Hybrid systems; Optimal control; Reachability; Safety; Stochastic systems

Indexed keywords

CONTINUOUS TIME SYSTEMS; CONTROL SYSTEMS; DISCRETE TIME CONTROL SYSTEMS; DYNAMIC PROGRAMMING; ELECTRIC GROUNDING; HYBRID COMPUTERS; HYBRID SENSORS; PROBABILITY; STATE SPACE METHODS; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC PROGRAMMING; SYSTEMS ENGINEERING;

HYBRID SYSTEMS; OPTIMAL CONTROL; REACHABILITY; SAFETY; STOCHASTIC SYSTEMS;

PROBLEM SOLVING;

EID: 52349103145     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2008.03.027     Document Type: Article

References (36)

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)
2. Alur R., Henzinger T., Lafferriere G., and Pappas G.J. Discrete abstractions of hybrid systems. Proceedings of the IEEE 88 2 (2000) 971-984
3. Asarin E., Bournez O., Dang T., and Maler O. Approximate reachability analysis of piecewise linear dynamical systems. In: Lynch N., and Krogh B. (Eds). Hybrid systems: Computation and control. Lecture notes in computer science Vol. 1790 (2000), Springer Verlag 21-31
4. Balluchi A., Benvenuti L., Di Benedetto M.D., Miconi G.M., Pozzi U., Villa T., et al. Maximal safe set computation for idle speed control of an automotive engine. In: Lynch N., and Krogh B. (Eds). Hybrid systems: Computation and control. Lecture notes in computer science Vol. 1790 (2000), Springer Verlag 32-44
5. Belta C., Finin P., Habets L., Halász A., Imielinski M., Kumar V., et al. Understanding the bacterial stringent response using reachability analysis of hybrid systems. In: Alur R., and Pappas G.J. (Eds). Hybrid systems: Computation and control. Lecture notes in computer science Vol. 2993 (2004), Springer Verlag 111-126
6. Bertsekas D.P. Infinite-time reachability of state-space regions using feedback control. IEEE Transactions on Automatic Control AC-17 5 (1972) 604-613
7. Bertsekas D.P., and Shreve S.E. Stochastic optimal control: The discrete-time case (1996), Athena Scientific
8. Bujorianu M.L. Extended stochastic hybrid systems and their reachability problem. In: Alur R., and Pappas G. (Eds). Hybrid systems: Computation and control. Lecture notes in computer science Vol. 2993 (2004), Springer Verlag 234-249
9. Bujorianu, M. L., & Lygeros, J. (2004). General stochastic hybrid systems: Modelling and optimal control. In Proceedings of the 43rd IEEE conference on decision and control
10. Davis M.H.A. Markov models and optimization (1993), Chapman & Hall/CRC Press, London
11. Digailova, I. A., & Kurzhanski, A. B. (2005). Reachability analysis under control-dependent stochastic noise. In Proceedings of the 16th IFAC world congress
12. Fehnker A., and Ivančić F. Benchmarks for hybrid systems verifications. In: Alur R., and Pappas G.J. (Eds). Hybrid systems: Computation and control. Lecture notes in computer science Vol. 2993 (2004), Springer Verlag 326-341
13. Ghosh M.K., Araposthasis A., and Marcus S.I. Ergodic control of switching diffusions. SIAM Journal of Control and Optimization 35 6 (1997) 1952-1988
14. Girard A. Reachability of uncertain linear systems using zonotopes. In: Morari M., and Thiele L. (Eds). Hybrid systems: Computation and control. Lecture notes in computer science Vol. 3414 (2005), Springer Verlag 291-305
15. Girard, A., Julius, A., & Pappas, G. J. (2006). Approximate simulation relations for hybrid systems. In Proceedings of the 2nd IFAC conference on analysis and design of hybrid systems
16. Hu J., Lygeros J., and Sastry S. Towards a theory of stochastic hybrid systems. In: Lynch N., and Krogh B. (Eds). Hybrid systems: Computation and control. Lecture notes in computer science Vol. 1790 (2000), Springer Verlag 160-173
17. Hu J., Prandini M., and Sastry S. Aircraft conflict prediction in the presence of a spatially correlated wind field. IEEE Transactions on Intelligent Transportation Systems 3 (2005) 326-340
18. Katoen J.P. Stochastic model checking. In: Cassandras C.G., and Lygeros J. (Eds). Stochastic hybrid systems. Automation and control engineering series Vol. 24 (2006), Taylor & Francis Group/CRC Press 79-106
19. Kumar P.R., and Varaiya P.P. Stochastic systems: Estimation, identification, and adaptive control (1986), Prentice Hall, Inc, New Jersey
20. Kurzhanski A.B., and Varaiya P. On reachability under uncertainty. SIAM Journal of Control and Optimization 41 1 (2002) 181-216
21. Kushner H.J., and Dupuis P.G. Numerical methods for stochastic control problems in continuous time (2001), Springer-Verlag, New York
22. Lygeros J. On reachability and minimum cost optimal control. Automatica 40-6 (2004) 317-927
23. Lygeros J., Tomlin C., and Sastry S. Controllers for reachability specifications for hybrid systems. Automatica 35 3 (1999) 349-370
24. Lygeros, J., & Watkins, O. (2003). Stochastic reachability for discrete time systems: an application to aircraft collision avoidance. In Proceedings of the 42nd IEEE conference of decision and control
25. Malhame R., and Chong C.-Y. Electric load model synthesis by diffusion approximation of a high-order hybrid-state stochastic system. IEEE Transactions on Automatic Control 30 9 (1985) 854-860
26. Mitchell I., and Templeton J. A toolbox of Hamilton-Jacobi solvers for analysis of nondeterministic continuous and hybrid systems. In: Morari M., and Thiele L. (Eds). Hybrid systems: Computation and control. LNCIS Vol. 3414 (2005), Springer Verlag 480-494
27. Mitchell I., and Tomlin C. Level set methods for computation in hybrid systems. In: Krogh B., and Lynch N. (Eds). Hybrid systems: Computation and control. Lecture notes in computer science (2000), Springer Verlag 310-323
28. Picasso B., and Bicchi A. Control synthesis for practical stabilization of quantized linear systems. Rendiconti Seminario Matematico Università di Torino 63 4 (2005) 397-410
29. Prajna S., Jadbabaie A., and Pappas G.J. A framework for worst-case and stochastic safety verification using barrier certificates. IEEE Transactions on Automatic Control 52 8 (2007) 1415-1429
30. Prandini M., and Hu J. A stochastic approximation method for reachability computations. In: Blom H.A.P., and Lygeros J. (Eds). Stochastic hybrid systems: Theory and safety applications. Lecture notes in control and informations sciences Vol. 337 (2006), Springer 107-139
31. Prandini M., and Hu J. Stochastic reachability: Theory and numerical approximation. In: Cassandras C.G., and Lygeros J. (Eds). Stochastic hybrid systems. Automation and control engineering series Vol. 24 (2006), Taylor & Francis Group/CRC Press 107-138
32. Prandini M., Hu J., Lygeros J., and Sastry S. A probabilistic approach to aircraft conflict detection. IEEE Transactions on Intelligent Transportation Systems 1 4 (2000) 199-220
33. Puterman M.L. Markov decision processes (1994), John Wiley & Sons, Inc
34. Stursberg O., and Krogh B.H. Effcient representation and computation of reachable sets for hybrid systems. In: Pnueli A., and Maler O. (Eds). Hybrid systems: Computation and control. Lecture notes in computer science Vol. 2623 (2003), Springer Verlag 482-497
35. Tomlin C., Lygeros J., and Sastry S. Synthesizing controllers for nonlinear hybrid systems. In: Henzinger T., and Sastry S. (Eds). Hybrid systems: Computation and control. Lecture notes in computer science Vol. 1386 (1998), Springer Verlag 360-373
36. Tomlin C., Mitchell I., Bayen A., and Oishi M. Computational techniques for the verification and control of hybrid systems. Proceedings of the IEEE 91 7 (2003) 986-1001