Reachability of uncertain linear systems using zonotopes

Lecture Notes in Computer Science

Volumn 3414, Issue , 2005, Pages 291-305

  Girard, Antoine ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; ENCODING (SYMBOLS); HYBRID COMPUTERS; MATHEMATICAL TRANSFORMATIONS; SET THEORY;

LINEAR HYBRID SYSTEMS; LINEAR TRANSFORMATION; POLYTOPES; VERIFICATION; ZONOTOPES;

LINEAR SYSTEMS;

EID: 24344472268     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-540-31954-2_19     Document Type: Conference Paper

References (22)

1. R. Alur, T. Dang, F. Ivancic, Reachability analysis of hybrid systems via predicate abstraction, Hybrid Systems: Computation and Control, C.J. Tomlin, M.R. Greenstreet (Eds), no. 2289 in LNCS, pp 35-48, 2002.
2. E. Asarin, O. Bournez, T. Dang, O. Maler, Approximate reachability analysis of piecewise linear dynamical systems, Hybrid Systems: Computation and Control, N. Lynch, B. H. Krogh (Eds), no. 1790 in LNCS, pp 21-31, Springer, 2000.
3. E. Asarin, T. Dang, O. Maler, d/dt: A verification tool for hybrid systems, in the Proc. of CDC'01, 2001.
4. E. Asarin, G. Schneider, S.Yovine. Towards computing phase portraits of polygonal differential inclusions, Hybrid Systems: Computation and Control, C.J. Tomlin, M.R. Greenstreet (Eds), no. 2289 in LNCS, pp 49-61, 2002.
5. E. Asarin, T. Dang, A. Girard, Reachability of non-linear systems using conservative approximations, Hybrid Systems: Computation and Control, O. Maler, A. Pnueli (Eds), no. 2623 in LNCS, pp 22-35, Spinger, 2003.
6. E. Asarin, T. Dang, Abstraction by projection and application to multi-affine systems, Hybrid Systems: Computation and Control, R. Alur, G.J. Pappas (Eds), no. 2993 in LNCS, pp 32-47, Springer, 2004.
7. A. Chutinan, B.H. Krogh, Verification of polyhedral invariant hybrid automata using polygonal flow pipe approximations. Hybrid Systems: Computation and Control, F. Vaandrager, J. van Schuppen (Eds), no. 1569 in LNCS, pp 76-90, Springer, 1999.
8. A. Chutinan, B.H. Krogh, Computational techniques for hybrid system verification, IEEE Trans. on Automatic Control, vol. 48, no. 1, 2003, pp. 64-75.
9. Combastel C., A state bounding observer based on zonotopes, in Proc. of European Control Conference, 2003.
10. T. Dang, Vérification et synthèse des systèmes hybrides, Thèse de Doctorat, Institut National Polytechnique de Grenoble, 2000.
11. L.J. Guibas, A. Nguyen, L. Zhang, Zonotopes as bounding volumes, in Proc. of Symposium on Discrete Algorithms, pp 803-812.
12. B. Huber and B. Sturmfels, A polyhedral method for solving sparse polynomial systems, Math. of Computation, 64:1541-1555, 1995.
13. W. Kühn, Zonotope dynamics in numerical quality control, in Mathematical Visualization, H.-C. Hege, K. Polthier (Eds), pp 125-134, Springer, 1998.
14. A. Kurzhanski, P. Varaiya, Ellipsoidal tehcniques for reachability analysis, Hybrid Systems: Computation and Control, N. Lynch, B. H. Krogh (Eds), no. 1790 in LNCS, Springer, 2000.
15. G. Lafferriere, G. Pappas, S. Yovine, Reachability computation for linear systems, Proc. IFAC World Congress, E:7-12, 1999.
16. I. Mitchell, C. Tomlin, Level set methods for computation in hybrid systems, Hybrid Systems: Computation and Control, N. Lynch, B. H. Krogh (Eds), no. 1790 in LNCS, Springer, 2000.
17. M. Rubensson, B. Lennartson, S. Pettersson, Convergence to limit cycles in hybrid systems: an example, Large Scale Systems: Theory and Applications, pp 704-709, 1998.
18. O. Stursberg, B.H. Krogh, Efficient representation and computation of reachable sets for hybrid systems, Hybrid Systems: Computation and Control, O. Maler, A. Pnueli (Eds), no. 2623 in LNCS, pp 482-497, Spinger, 2003.
19. C. Tomlin, I. Mitchell, A. Bayen, and M. Oishi, Computational techniques for the verification and control of hybrid systems, Proc. of the IEEE, 91(7):986-1001, July 2003.
20. A. Tiwari, G. Khanna, Series of abstractions for hybrid automata, Hybrid Systems: Computation and Control, C.J. Tomlin, M.R. Greenstreet (Eds), no. 2289 in LNCS, pp 465-478, 2002.
21. H. Yazarel, G.J. Pappas, Geometric programming relaxations for linear system reachability, in Proc. American Control Conference, 2004.
22. G.M. Ziegler, Lectures on polytopes, Graduate texts in Mathematics, Springer-Verlag, 1995.