Reachability analysis of large-scale affine systems using low-dimensional polytopes

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

Volumn 3927 LNCS, Issue , 2006, Pages 287-301

  Han, Zhi ^a   Krogh, Bruce H ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; LARGE SCALE SYSTEMS; SET THEORY;

KRYLOV SUBSPACE; LARGE-SCALE AFFINE SYSTEMS; POLYTOPES;

COMPUTATIONAL METHODS;

EID: 33745778046     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11730637_23     Document Type: Conference Paper

References (16)

1. Girard, A.: Reachability of uncertain linear systems using zonotopes. In: Hybrid Systems: Computation and Control (HSCC'05). (2005) 291-305
2. Stursberg, O., Krogh, B.H.: On efficient representation and computation of reachable sets for hybrid systems. In: Hybrid Systems: Computation and Control (HSCC'03). (2003) 482-497
3. Asarin, E., Dang, T.: Abstraction by projection and application to multi-affine systems. In: Proceedings of Hybrid Systems: Computation and Control (HSCC'04). (2004) 32-47
4. Girard, A., Pappas, G.J.: Approximation metrics for discrete and continuous systems. Technical Report MS-CIS-05-10, Dept. of CIS, University of Pennsylvania (2005)
5. Bemporad, A., Pilippi, C., Torrisi, F.D.: Inner and outer approximation of polytopes using boxes. Computational Geometry: Theory and Applications 27(2) (2003) 151-178
6. Kurzhanski, A.B., Varaiya, P.: Ellipsoidal techniques for reachability analysis. In: Hybrid Systems: Computation and Control (HSCC'00). (2000) 202-214
7. Ma, J.D., Rutenbar, R.A.: Interval-valued reduced order statistical interconnect modeling. In: Computer Aided Design, 2004. IEEE/ACM International Conference on. (2004) 1092-3152
8. de Figueiredo, L.H., Stolf, J.: Self-Validated Numerical Methods and Applications. Brazilian Mathematics Colloquium monograph, IMPA, Rio de Janeiro, Brazil (1997)
9. Saad, Y.: Analysis of some Krylov subspace approximations to the matrix exponential operator. SIAM Journal of Numerical Analysis 20(1) (1992) 209-228
10. Grünbaum, B.: Convex Polytopes (Second Edition). Springer-Verlag New York, Inc. (2003)
11. Chutinan, A., Krogh, B.H.: Compuational techniques for hybrid system verification. IEEE Transaction on Automatic Control 48(1) (2003) 64-75
12. Moler, C., Van Loan, C.: Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review 45(1) (2003) 3-49
13. Sidje, R.B.: EXPOKIT: Software package for computing matrix exponentials. ACM Transactions on Mathematical Software 24(1) (1998) 130-156
14. Golub, G.H., Van Loan, C.F.: Matrix Computations (Third Edition). The John Hopkins University Press (1996)
15. Han, Z.: Reachability analysis of continuous dynamic systems using dimension reduction and decomposition. PhD thesis, Carnegie Mellon University (2005)
16. Farlow, S.J.: Partial Differential Equations for Scientists and Engineers. Dover Publications, Inc. (1993)