Reachable set computation for uncertain time-varying linear systems

HSCC'11 - Proceedings of the 2011 ACM/SIGBED Hybrid Systems: Computation and Control

Volumn , Issue , 2011, Pages 93-102

  Althoff, Matthias ^a   Le Guernic, Colas ^b   Krogh, Bruce H ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

Linear systems; Peano Baker series; Reachability analysis; Safety; Uncertain parameters

Indexed keywords

APPROXIMATION ERRORS; GAIN-SCHEDULED CONTROLLERS; HYBRID DYNAMICS; HYBRID MODEL; INTERVAL MATRIX; MATRIX; PEANO-BAKER SERIES; POLYTOPES; REACHABILITY ANALYSIS; REACHABLE SET; SAFETY; TIME VARYING LINEAR SYSTEMS; TIME VARYING PARAMETER; UNCERTAIN PARAMETERS; ZONOTOPES;

COMPUTATIONAL EFFICIENCY; CONTROLLERS; HYBRID COMPUTERS; HYBRID SYSTEMS; LINEAR SYSTEMS; TIME VARYING CONTROL SYSTEMS; UNCERTAINTY ANALYSIS;

MATRIX ALGEBRA;

EID: 79955988358     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1967701.1967717     Document Type: Conference Paper

References (27)

1. M. Althoff. Reachability Analysis and its Application to the Safety Assessment of Autonomous Cars. PhD thesis, TU München, 2010.
2. M. Althoff, O. Stursberg, and M. Buss. Reachability analysis of nonlinear systems with uncertain parameters using conservative linearization. In Proc. of the 47th IEEE Conference on Decision and Control, pages 4042-4048, 2008.
3. M. Althoff, O. Stursberg, and M. Buss. Computing reachable sets of hybrid systems using a combination of zonotopes and polytopes. Nonlinear Analysis: Hybrid Systems, 4:233-249, 2010.
4. E. Asarin, T. Dang, and O. Maler. d/dt: A verification tool for hybrid systems. In Proc. of the Conference on Decision and Control, pages 2893-2898, 2001. (Pubitemid 34139405)
5. A. Chutinan and B. H. Krogh. Computational techniques for hybrid system verification. In IEEE Transactions on Automatic Control, volume 48, pages 64-75, 2003.
6. T. Dang. Vérification et synthèse des systèmes hybrides. PhD thesis, Institut National Polytechnique de Grenoble, 2000.
7. Goran Frehse. PHAVer: Algorithmic verification of hybrid systems past HyTech. In Hybrid Systems: Computation and Control, LNCS 3413, pages 258-273. Springer, 2005. (Pubitemid 41252072)
8. P. Gaspar, I. Szaszi, and J. Bokor. The design of a combined control structure to prevent the rollover of heavy vehicles. European Journal of Control, 10:1-15, 2004.
9. A. Girard. Reachability of uncertain linear systems using zonotopes. In Hybrid Systems: Computation and Control, LNCS 3414, pages 291-305. Springer, 2005. (Pubitemid 41252074)
10. A. Girard and C. Le Guernic. Efficient reachability analysis for linear systems using support functions. In Proc. of the 17th IFAC World Congress, pages 8966-8971, 2008.
11. A. Girard and C. Le Guernic. Zonotope/hyperplane intersection for hybrid systems reachability analysis. In Proc. of Hybrid Systems: Computation and Control, LNCS 4981, pages 215-228. Springer, 2008.
12. A. Girard, C. Le Guernic, and O. Maler. Efficient computation of reachable sets of linear time-invariant systems with inputs. In Hybrid Systems: Computation and Control, LNCS 3927, pages 257-271. Springer, 2006. (Pubitemid 44019592)
13. T. Henzinger. The theory of hybrid automata, volume 170 of NATO ASI Series F: Computer and Systems Sciences, pages 265-292. Springer, 2000.
14. T. A. Henzinger, P.-H. Ho, and H. Wong-Toi. Algorithmic analysis of nonlinear hybrid systems. IEEE Transactions on Automatic Control, 43:540-554, 1998. (Pubitemid 128737377)
15. T. A. Henzinger, B. Horowitz, R. Majumdar, and H. Wong-Toi. Beyond HyTech: Hybrid systems analysis using interval numerical methods. In Hybrid Systems: Computation and Control, LNCS 1790, pages 130-144. Springer, 2000.
16. L. Jaulin, M. Kieffer, and O. Didrit. Applied Interval Analysis. Springer, 2006.
17. W. Kühn. Rigorously computed orbits of dynamical systems without the wrapping effect. Computing, 61:47-67, 1998. (Pubitemid 128508169)
18. A. B. Kurzhanskiy and P. Varaiya. Ellipsoidal techniques for reachability analysis of discrete-time linear systems. IEEE Transactions on Automatic Control, 52:26-38, 2007. (Pubitemid 46343995)
19. G. Lafferriere, G. J. Pappas, and S. Yovine. Symbolic reachability computation for families of linear vector fields. Symbolic Computation, 32:231-253, 2001. (Pubitemid 33098464)
20. D. J. Leith and W. E. Leithead. Survey of gain-scheduling analysis and design. International Journal of Control, 73:1001-1025, 2000. (Pubitemid 35395388)
21. N. S. Nedialkov and K. R. Jackson. Perspectives on Enclosure Methods, chapter A New Perspective on the Wrapping Effect in Interval Methods for Initial Value Problems for Ordinary Differential Equations, pages 219-264. Springer-Verlag, 2001.
22. N. Ramdani, N. Meslem, and Y. Candau. Reachability analysis of uncertain nonlinear systems using guaranteed set integration. In Proc. of the 17th IFAC World Congress, pages 8972-8977, 2008.
23. N. Ramdani, N. Meslem, and Y. Candau. Reachability of uncertain nonlinear systems using a nonlinear hybridization. In Hybrid Systems: Computation and Control, LNCS 4981, pages 415-428. Springer, 2008.
24. N. Ramdani, N. Meslem, and Y. Candau. Computing reachable sets for uncertain nonlinear monotone systems. Nonlinear Analysis: Hybrid Systems, 4:263-278, 2010.
25. W. J. Rugh. Linear System Theory. Prentice Hall, 1996.
26. O. Stursberg and B. H. Krogh. Efficient representation and computation of reachable sets for hybrid systems. In Hybrid Systems: Computation and Control, LNCS 2623, pages 482-497. Springer, 2003.
27. C. Tomlin, I. Mitchell, A. Bayen, and M. Oishi. Computational techniques for the verification and control of hybrid systems. In Proceedings of the IEEE, volume 91, pages 986-1001, 2003. (Pubitemid 40890836)