The reachability problem for uncertain hybrid systems revisited: A viability theory perspective

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3927 LNCS, Issue , 2006, Pages 242-256

  Gao, Yan ^a   Lygeros, John ^b   Quincapoix, Marc ^c  

^a UNIVERSITY OF SHANGHAI FOR SCIENCE AND TECHNOLOGY   (China)

^b UNIVERSITY OF PATRAS   (Greece)

^c UNIVERSITÉ DE BRETAGNE OCCIDENTALE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; PROBLEM SOLVING;

HYBRID STRATEGY; HYBRID SYSTEMS; NON-SMOOTH ANALYSIS; VIABILITY THEORY;

HYBRID COMPUTERS;

EID: 33745794493     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11730637_20     Document Type: Conference Paper

References (27)

1. W. Thomas, "On the synthesis of strategies in infinite games," in Proceedings of STAGS 95, ser. LNCS, E. Mayr and C. Puech, Eds. Berlin: Springer-Verlag, 1995, vol. 900, pp. 1-13.
2. P. J. G. Ramadge and W. M. Wonham, "The control of discrete event systems," Proceedings of the IEEE, vol. Vol.77, no. 1, pp. 81-98, 1989.
3. O. Maler, A. Pnueli, and J. Sifakis, "On the synthesis of discrete controllers for timed systems," in Theoretical Aspects of Computer Science, ser. LNCS, no. 900. Berlin: Springer-Verlag, 1995, pp. 229-242.
4. M. Heymann, F. Lin, and G. Meyer, "Synthesis and viability of minimally interventive legal controllers for hybrid systems," Discrete Event Dynamic Systems: Theory and Applications, vol. 8, no. 2, pp. 105-135, June 1998.
5. H. Wong-Toi, "The synthesis of controllers for linear hybrid automata," in IEEE Conference on Decision and Control, San Diego, California, December 10-12 1997, pp. 4607-4613.
6. J. Lygeros, D. Godbole, and S. Sastry, "Verified hybrid controllers for automated vehicles," IEEE Transactions on Automatic Control, vol. 43, no. 4, pp. 522-539, April 1998.
7. J. Lygeros, C. Tomlin, and S. Sastry, "Controllers for reachability specifications for hybrid systems," Automatica, vol. 35, no. 3, pp. 349-370, March 1999.
8. C. Tomlin, J. Lygeros, and S. Sastry, "A game theoretic approach to controller design for hybrid systems," Proceedings of the IEEE, vol. 88, no. 7, pp. 949-969, July 2000.
9. C. Tomlin, "Hybrid control of air traffic management systems," Ph.D. dissertation, Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, 1998.
10. I. M. Mitchell, "Application of level set methods to control and reachability problems in continuous and hybrid systems," Ph.D. dissertation, Stanford University, 2002.
11. L. Evans and P. Souganidis, "Differential games and representation formulas for solutions of Hamilton-Jacobi-Isaacs equations," Indiana University Mathematics Journal, vol. 33, no. 5, pp. 773-797, 1984.
12. J. Lygeros, "On reachability and minimum cost optimal control," Automation, vol. 40, no. 6, pp. 917-927, 2004.
13. I. Mitchell, A. Bayen, and C. Tomlin, "A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games," IEEE Transactions on Automatic Control, vol. 70, no. 7, pp. 947-957, 2005.
14. P. Cardaliaguet, "Domaines discriminants et jeux différentiels," Ph.D. dissertation, Université Paris IX Dauphine, 1993.
15. _, "A differential game with two players and one target," SIAM Journal on Control and Optimization, vol. 34, no. 4, pp. 1441-1460, 1996.
16. P. Cardaliaguet, M. Quincampoix, and P. Saint-Pierre, "Pursuit differential games with state constraints," SIAM Journal on Control and Optimization, vol. 39, no. 5, pp. 1615-1632, 2001.
17. E. Crück, "Contrôle et jeux différentiels des systèmes hybrides et impulsionnels: Problèmes de cible at de viabilité," Ph.D. dissertation, Université de Bretagne Occidentale, 2003.
18. P. Cardaliaguet, M. Quincampoix, and P. Saint-Pierre, "Set-valued numerical analysis for optimal control and differential games," in Stochastic and Differential Games: Theory and Numerical Methods, ser. Annals of the International Society of Dynamic Games, M. Bardi, T. Raghavan, and T. Parthasarathy, Eds. Boston, MA: Birkhäuser, 1999, no. 4, pp. 177-247.
19. _, "Numerical schemes for discontinuous value functions of optimal control," Set-Valued Analysis, vol. 8, pp. 111-126, 2000.
20. J.-P. Aubin, J. Lygeros, M. Quincampoix, S. Sastry, and N. Seube, "Impulse differential inclusions: A viability approach to hybrid systems," IEEE Transactions on Automatic Control, vol. 47, no. 1, pp. 2-20, January 2002.
21. Y. Gao, J. Lygeros, M. Quincampoix, and N. Seube, "On the control of uncertain impulsive systems: Approximate stabilization and controlled invariance," International Journal of Control, vol. 77, no. 16, pp. 1393-1407, 2004.
22. J.-P. Aubin and H. Frankowska, Set- Valued Analysis. Boston, MA: Birkhäuser, 1990.
23. J. Lygeros, K. Johansson, S. Simić, J. Zhang, and S. Sastry, "Dynamical properties of hybrid automata," IEEE Transactions on Automatic Control, vol. 48, no. 1, pp. 2-17, January 2003.
24. R. Goebel, J. Hespanha, A. Teel, C. Cai, and R. Sanfelice, "Hybrid systems: Generalized solutions and robust stability," in IFAC Symposium on Nonlinear Control Systems, September 2004.
25. P. Varaiya, "On the existance of solutions to a differential game," SIAM Journal on Control, vol. 5, no. 1, pp. 153-162, 1967.
26. P. Cardaliaguet, "Nonsmooth semi-permeable barriers, isaacs equation and application to a differential game with one target and two players," Applied Mathematics and Optimization, vol. 36, pp. 125-146, 1997.
27. C. Tomlin, I. Mitchell, and R. Ghosh, "Safety verification of conflict resolution manoeuvres," IEEE Transactions on Intelligent Transportation Systems, vol. 2, no. 2, pp. 110-120, June 2001.