Computation of an over-approximation of the backward reachable set using subsystem level set functions

European Control Conference, ECC 2003

Volumn , Issue , 2003, Pages 300-305

  Stipanović, Dušan M ^a   Hwang, Inseok ^a   Tomlin, Claire J ^a  

^a 496 Lomita Mall   (United States)

Author keywords

Differential games; Interconnected systems; Over approximations; Reachable set

Indexed keywords

GAME THEORY; LARGE SCALE SYSTEMS; ROTATIONAL FLOW; SET THEORY;

AIRCRAFT CONFLICT RESOLUTION; COMPUTATION TIME; COMPUTATIONAL PROBLEM; DIFFERENTIAL GAMES; LEVEL SET FUNCTIONS; OVER-APPROXIMATIONS; REACHABLE SET; SUBSYSTEM LEVEL;

NUMERICAL METHODS;

EID: 84949095766     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.23919/ecc.2003.7084971     Document Type: Conference Paper

References (21)

1. M. G. Crandall, L. C. Evans, and P.-L. Lions. Some properties of viscosity solutions of Hamilton-Jacobi equations. Transactions of American Mathematical Society, Vol. 282, No. 2, pp. 487-502, 1984.
2. I. Hwang, D. M. Stipanovi, and C. J. Tomlin. Applications of polytopic approximations of reachable sets to linear dynamic games and a class of nonlinear systems. Proceedings of the American Control Conference, Denver, Colorado, June 4-6, 2003, pp. 4613-4619.
3. M. M. Khrustalev. Exact description of reachable sets and global optimality conditions. Avtomatika i Telemekhanika, No. 5, pp. 62-70, 1988.
4. M. M. Khrustalev. Exact description of reachable sets and global optimality conditions II: conditions of global optimality. Avtomatika i Telemekhanika, No. 7, pp. 70-80, 1988.
5. V. F. Krotov. Global Methods in Optimal Control Theory. Marcel Dekker, Inc., New York, NY, 1996.
6. A. Kurzhanski and P. Varaiya. Ellipsoidal techniques for reachability analysis. In Hybrid Systems: Computation and Control (B. Krogh and N. Lynch, eds.), No. 1790 in Lecture Notes in Computer Science, pp. 202-214, Springer Verlag, 2000.
7. A. Kurzhanski and P. Varaiya. Dynamic optimization for reachability problems. Journal of Optimization Theory and Applications, Vol. 108, No. 2, pp. 227-251, 2001.
8. A. Kurzhanski and P. Varaiya. On reachability under uncertainty. SIAM Journal on Control and Optimization, Vol. 41, No. 1, pp. 181-216, 2002.
9. A. Kurzhanski and P. Varaiya. Reachability analysis for uncertain systems-the ellipsoidal technique. Dynamics of Continuous, Discrete & Impulse Systems, Series B: Applications & Algorithms, Vol. 9, No. 3, 347-367, 2002.
10. G. Leitmann. An Introduction to Optimal Control. McGraw-Hill, New York, NY, 1967.
11. J. Lygeros, C. J. Tomlin, and S. Sastry. Controllers for reachability specifications for hybrid systems. Automatica, Vol. 35, No. 3, pp. 349-370, 1999.
12. I. Mitchell, A. M. Bayen, and C. J. Tomlin. Validating a Hamilton-Jacobi approximation to hybrid system reachable sets. In Hybrid Systems: Computation and Control (M. D. D. Benedetto and A. Sangiovanni-Vincentelli, eds.), No. 2034 in Lecture Notes in Computer Science, pp. 418-432, Springer Verlag, 2001.
13. I. Mitchell, A. M. Bayen, and C. J. Tomlin. Computing reachable sets for continuous dynamic games using level set methods. Submitted for publication in the IEEE Transactions on Automatic Control, December 2001.
14. th birthday, 2003.
15. S. Sastry. Nonlinear Systems: Analysis, Stability, and Control. Springer-Verlag, New York, NY, 1999.
16. D. M. Stipanovi, G. nalhan, R. Teo, and C. J. Tomlin. Decentralized Overlapping Control of a Formation of Unmanned Aerial Vehicles. Proceedings of the 2002 IEEE Conference on Decision and Control, Las Vegas, Nevada, December 10-13, 2002, pp. 2829-2835.
17. C. J. 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. 949-970, 2000.
18. P. Varaiya. Reach set computation using optimal control. In Proceedings of the KIT Workshop on Verification of Hybrid Systems, Verimag, Grenoble, France, 1998.
19. T. L. Vincent and Z. Y. Wu. Estimating projections of the controllable set. Journal of Guidance, Control, and Dynamics, Vol. 13, No. 3, pp. 572-575, 1990.
20. T. L. Vincent and W. J. Grantham. Nonlinear and Optimal Control Systems. John Wiley & Sons, Inc., New York, NY, 1997.
21. R. Vinter. A characterization of the reachable set for nonlinear control systems. SIAM Journal on Control and Optimization, Vol. 18, No. 6, pp. 599-610, 1980.