Level set methods for computation in hybrid systems

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

Volumn 1790, Issue , 2000, Pages 310-323

  Mitchell, Ian ^a   Tomlin, Claire J ^b  

^a STANFORD UNIVERSITY   (United States)

^b 496 Lomita Mall   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; CONTROL SYSTEM ANALYSIS; DROP BREAKUP; HYBRID SYSTEMS; LEVEL MEASUREMENT;

CONTINUOUS STATE; KEY EQUATION; LEVEL SET METHOD; NONLINEAR HYBRID SYSTEMS; NUMERICAL SOLUTION; REACHABILITY; REACHABILITY ANALYSIS; REACHABLE SET;

NUMERICAL METHODS;

EID: 84974725120     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-46430-1_27     Document Type: Conference Paper

References (23)

1. R. Alur and D. Dill, “A theory of timed automata”, Theoretical Computer Science, vol. 126, pp. 183-235, 1994.
2. R. Alur, C. Courcoubetis, T. A. Henzinger, and P.-H. Ho, “Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems”, in Hybrid Systems (R. L. Grossman, A. Nerode, A. P. Ravn, and H. Rischel, eds.), LNCS, pp. 366-392, New York: Springer Verlag, 1993.
3. T. A. Henzinger, P. H. Ho, and H. Wong-Toi, “A user guide to HYTECH”, in TACAS 95: Tools and Algorithms for the Construction and Analysis of Systems (E. Brinksma, W. Cleaveland, K. Larsen, T. Margaria, and B. Steffen, eds.), no. 1019 in LNCS, pp. 41-71, Springer Verlag, 1995.
4. C. Daws, A. Olivero, S. Tripakis, and S. Yovine, “The tool KRONOS”, in Hybrid Systems III, Verification and Control, no. 1066 in LNCS, pp. 208-219, Springer Verlag, 1996.
5. O. Maler, A. Pnueli, and J. Sifakis, “On the synthesis of discrete controllers for timed systems”, in STACS 95: Theoretical Aspects of Computer Science (E. W. Mayr and C. Puech, eds.), no. 900 in LNCS, pp. 229-242, Munich: Springer Verlag, 1995.
6. H. Wong-Toi, “The synthesis of controllers for linear hybrid automata”, in Proceedings of the IEEE Conference on Decision and Control, (San Diego, CA), 1997.
7. A. Deshpande, Control of Hybrid Systems. PhD thesis, Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, 1994.
8. J. Lygeros, Hierarchical, Hybrid Control of Large Scale Systems. PhD thesis, Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, 1996.
9. C. Tomlin, J. Lygeros, and S. Sastry, “Synthesizing controllers for nonlinear hybrid systems”, in Hybrid Systems: Computation and Control (T. Henzinger and S. Sastry, eds.), no. 1386 in LNCS, pp. 360-373, New York: Springer Verlag, 1998.
10. J. Lygeros, C. Tomlin, and S. Sastry, “On controller synthesis for nonlinear hybrid systems”, in Proceedings of the IEEE Conference on Decision and Control, (Tampa, FL), pp. 2101-2106, 1998.
11. C. J. Tomlin, Hybrid Control of Air Traffic Management Systems. PhD thesis, Department of Electrical Engineering, University of California, Berkeley, 1998.
12. M. Greenstreet and I. Mitchell, “Integrating projections”, in Hybrid Systems: Computation and Control (S. Sastry and T. Henzinger, eds.), no. 1386 in LNCS, pp. 159-174, Springer Verlag, 1998.
13. T. Dang and O. Maler, “Reachability analysis via face lifting”, in Hybrid Systems: Computation and Control (S. Sastry and T. Henzinger, eds.), no. 1386 in LNCS, pp. 96-109, Springer Verlag, 1998.
14. A. Chutinan and B. H. Krogh, “Verification of polyhedral-invariant hybrid automata using polygonal flow pipe approximations”, in Hybrid Systems: Computation and Control (F. Vaandrager and J. H. van Schuppen, eds.), no. 1569 in LNCS, pp. 76-90, New York: Springer Verlag, 1999.
15. A. B. Kurzhanski and P. Varaiya, “Ellipsoidal techniques for reachability analysis”, in Hybrid Systems: Computation and Control (B. Krogh and N. Lynch, eds.), LNCS (these proceedings), Springer Verlag, 2000.
16. O. Botchkarev and S. Tripakis, “Verification of hybrid systems with linear differential inclusions using ellipsoidal approximations”, in Hybrid Systems: Computation and Control (B. Krogh and N. Lynch, eds.), LNCS (these proceedings), Springer Verlag, 2000.
17. C. Tomlin, J. Lygeros, and S. Sastry, “Computing controllers for nonlinear hybrid systems”, in Hybrid Systems: Computation and Control (F. Vaandrager and J. H. van Schuppen, eds.), no. 1569 in LNCS, pp. 238-255, New York: Springer Verlag, 1999.
18. M. Bardi and I. Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman equations. Boston: Birkh auser, 1997.
19. S. Osher and J. A. Sethian, “Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations”, Journal of Computational Physics, vol. 79, pp. 12-49, 1988.
20. J. A. Sethian, Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision, and Materials Science. New York: Cambridge University Press, 1996.
21. M. G. Crandall and P.-L. Lions, “Viscosity solutions of Hamilton-Jacobi equations”, Transactions of the American Mathematical Society, vol. 277, no. 1, pp. 1-42, 1983.
22. M. G. Crandall, L. C. Evans, and P.-L. Lions, “Some properties of viscosity solutions of Hamilton-Jacobi equations”, Transactions of the American Mathematical Society, vol. 282, no. 2, pp. 487-502, 1984.
23. C. Tomlin, G. J. Pappas, and S. Sastry, “Conflict resolution for air traffic management: A case study in multi-agent hybrid systems”, IEEE Transactions on Automatic Control, vol. 43, pp. 509-521, April 1998.