Avoiding geometric intersection operations in reachability analysis of hybrid systems

HSCC'12 - Proceedings of the 15th ACM International Conference on Hybrid Systems: Computation and Control

Volumn , Issue , 2012, Pages 45-54

  Althoff, Matthias ^a   Krogh, Bruce H ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Guard intersection; Hybrid systems; Reachability analysis; Safety; Zonotopes

Indexed keywords

CONTINUOUS STATE; DISCRETE TRANSITIONS; HALF SPACES; INTERSECTION OPERATION; MECHANICAL SYSTEMS; NONLINEAR MAPPINGS; PIECEWISE-CONTINUOUS; REACHABILITY ANALYSIS; SYSTEM VERIFICATIONS; VERIFICATION TECHNIQUES; ZONOTOPES;

ACCIDENT PREVENTION; SEMANTICS;

HYBRID SYSTEMS;

EID: 84860643658     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2185632.2185643     Document Type: Conference Paper

References (30)

1. M. Althoff. Reachability Analysis and its Application to the Safety Assessment of Autonomous Cars. Dissertation, Technische Universiẗat M̈unchen, 2010. http://nbnresolving.de/urn/resolver.pl?urn:nbn:de:bvb:91- diss-20100715-963752-1-4.
2. M. Althoff and B. H. Krogh. Zonotope bundles for the efficient computation of reachable sets. In Proc. of the 50th IEEE Conference on Decision and Control, pages 6814-6821, 2011.
3. M. Althoff, C. Le Guernic, and B. H. Krogh. Reachable set computation for uncertain time-varying linear systems. In Hybrid Systems: Computation and Control, pages 93-102, 2011.
4. 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.
5. D. Avis, D. Bremner, and R. Seidel. How good are convex hull algorithms? Computational Geometry: Theory and Applications, 7:265-301, 1997. (Pubitemid 127371605)
6. R. Bagnara, P. M. Hill, and E. Zaffanella. The Parma Polyhedra Library: Toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems. Science of Computer Programming, 72:3-21, 2008.
7. O. Botchkarev and S. Tripakis. Verification of hybrid systems with linear differential inclusions using ellipsoidal approximations. In Hybrid Systems: Computation and Control, LNCS 1790, pages 73-88. Springer, 2000.
8. A. Chutinan and B. H. Krogh. Computational techniques for hybrid system verification. IEEE Transactions on Automatic Control, 48(1):64-75, 2003.
9. E. Clarke, A. Fehnker, Z. Han, B. Krogh, O. Stursberg, and M. Theobald. Tools and Algorithms for the Construction and Analysis of Systems, chapter Verification of Hybrid Systems based on Counterexample-Guided Abstraction Refinement, pages 192-207. LNCS 2619. Springer, 2003.
10. W. Damm, S. Disch, H. Hungar, S. Jacobs, J. Pang, F. Pigorsch, C. Scholl, U. Waldmann, and B. Wirtz. Exact state set representations in the verification of linear hybrid systems with large discrete state space. In Proc. of the 5th Int. Symposium on Automated Technology for Verification and Analysis, pages 425-440, 2007.
11. G. Frehse, C. Le Guernic, A. Donźe, S. Cotton, R. Ray, O. Lebeltel, R. Ripado, A. Girard, T. Dang, and O. Maler. Space Ex: Scalable verification of hybrid systems. In Proc. of the 23rd International Conference on Computer Aided Verification, LNCS 6806, pages 379-395. Springer, 2011.
12. A. Girard. Reachability of uncertain linear systems using zonotopes. In Hybrid Systems: Computation and Control, LNCS 3414, pages 291-305. Springer, 2005. (Pubitemid 41252074)
13. 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.
14. 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.
15. 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)
16. A. Hamadeh and J. Goncalves. Reachability analysis of continuous-time piecewise affine systems. Automatica, 44(12):189-3194, 2008.
17. T. A. Henzinger and P.-H. Ho. HyTech: The Cornell Hybrid Technology Tool. In Hybrid Systems II, LNCS 999, pages 265-294. Springer, 1995.
18. 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.
19. W. K̈uhn. Rigorously computed orbits of dynamical systems without the wrapping effect. Computing, 61:47-67, 1998. (Pubitemid 128508169)
20. A. A. Kurzhanskiy and P. Varaiya. Ellipsoidal techniques for reachability analysis of discrete-time linear systems. IEEE Transactions on Automatic Control, 52(1):26-38, 2007. (Pubitemid 46343995)
21. G. Lafferriere, G. J. Pappas, and S. Yovine. A new class of decidable hybrid systems. In Hybrid Systems: Computation and Control, LNCS 1569, pages 137-151. Springer, 1999.
22. A. Lagerberg. A benchmark on hybrid control of an automotive powertrain with backlash. Technical Report R005/2007, Signals and Systems, Chalmers University of Technology, 2007.
23. I. M. Mitchell, A. M. Bayen, and C. J. Tomlin. A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games. IEEE Transactions on Automatic Control, 50:947-957, 2005. (Pubitemid 41078397)
24. N. S. Nedialkov and M. von Mohrenschildt. Rigorous simulation of hybrid dynamic systems with symbolic and interval methods. In Proc. of the American Control Conference, pages 140-147, 2002.
25. M. Nordin and P.-O. Gutman. Controlling mechanical systems with backlash - a survey. Automatica, 38:1633 - 1649, 2002. (Pubitemid 34946681)
26. E.-A. M. A. Rabeih. Torsional Vibration Analysis of Automotive Drivelines. PhD thesis, University of Leeds, 1997.
27. S. V. Rakovíc, P. Grieder, M. Kvasnica, D. Q. Mayne, and M. Morari. Computation of invariant sets for piecewise affine discrete time systems subject to bounded disturbances. In Proc. of the 43rd IEEE Conference on Decision and Control, pages 1418-1423, 2004. (Pubitemid 40291155)
28. N. Ramdani and N. S. Nedialkov. Computing reachable sets for uncertain nonlinear hybrid systems using interval constraint-propagation techniques. Nonlinear Analysis: Hybrid Systems, 5(2):149-162, 2010.
29. F. M. Schlaepfer and F. C. Schweppe. Continuous-time state estimation under disturbances bounded by convex sets. IEEE Transactions on Automatic Control, 17(2):197-205, 1972.
30. 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.