Reachability analysis of nonlinear systems using conservative polynomialization and non-convex sets

HSCC 2013 - Proceedings of the 16th International Conference on Hybrid Systems: Computation and Control, Part of CPSWeek 2013

Volumn 1, Issue , 2012, Pages 173-182

  Althoff, Matthias ^a  

^a ILMENAU UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Difference inclusion; Hybrid systems; Nonlinear dynamics; Polynomial zonotopes; Reachability analysis

Indexed keywords

CONTINUOUS DYNAMICS; DIFFERENCE INCLUSIONS; LINEAR DIFFERENTIAL INCLUSIONS; LINEARIZATION TECHNIQUE; POLYNOMIAL COMPLEXITY; REACHABILITY ANALYSIS; SET REPRESENTATION; ZONOTOPES;

ABSTRACTING; DYNAMICS; HYBRID SYSTEMS; LINEARIZATION; POLYNOMIALS;

SET THEORY;

EID: 84876765932     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2461328.2461358     Document Type: Conference Paper

References (39)

1. M. Althoff. Reachability Analysis and its Application to the Safety Assessment of Autonomous Cars. Dissertation, Technische Universität München, 2010. http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:91- diss-20100715-963752-1-4.
2. M. Althoff and B. H. Krogh. Avoiding geometric intersection operations in reachability analysis of hybrid systems. In Hybrid Systems: Computation and Control, pages 45-54, 2012.
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. R. Alur and D. L. Dill. A theory of timed automata. Theoretical Computer Science, 126: 183-235, 1994.
6. E. Asarin, T. Dang, G. Frehse, A. Girard, C. Le Guernic, and O. Maler. Recent progress in continuous and hybrid reachability analysis. In Proc. of the 2006 IEEE Conference on Computer Aided Control Systems Design, pages 1582-1587, 2006.
7. E. Asarin, T. Dang, and A. Girard. Hybridization methods for the analysis of nonlinear systems. Acta Informatica, 43: 451-476, 2007.
8. G. Behrmann, A. David, K. G. Larsen, P. Pettersson, and W. Yi. Developing UPPAAL over 15 years. Softw., Pract. Exper., 41(2): 133-142, 2011.
9. M. Berz and G. Hoffstätter. Computation and application of Taylor polynomials with interval remainder bounds. Reliable Computing, 4: 83-97, 1998.
10. P. Bulychev, A. David, K. G. Larsen, A. Legay, G. Li, D. B. Poulsen, and A. Stainer. Monitor-based statistical model checking for weighted metric temporal logic. In Proc. of 18th International Conference on Logic for Programming Artificial Intel ligence and Reasoning, pages 168-182, 2012.
11. X. Chen, E. Ábráham, and G. Frehse. Efficient bounded reachability computation for rectangular automata. In 5th Workshop on Reachability Problems, LNCS 6945, pages 139-152. Springer, 2011.
12. X. Chen, S. Sankaranarayanan, and E. Ábrahám. Taylor model flowpipe construction for non-linear hybrid systems. In Proc. of the 33rd IEEE Real-Time Systems Symposium, 2012.
13. A. Chutinan and B. H. Krogh. Computational techniques for hybrid system verification. IEEE Transactions on Automatic Control, 48(1): 64-75, 2003.
14. E. Clarke, A. Fehnker, Z. Han, B. H. Krogh, J. Ouaknine, O. Stursberg, and M. Theobald. Abstraction and counterexample-guided refinement in model checking of hybrid systems. International Journal of Foundations of Computer Science, 14(4): 583-604, 2003.
15. E. M. Clarke and P. Zuliani. Statistical model checking for cyber-physical systems. In Proc. of the 9th International Symposium on Automated Technology for Verification and Analysis, LNCS 6996, pages 1-12, 2011.
16. T. Dang. V érification et synthèse des systèmes hybrides. PhD thesis, Institut National Polytechnique de Grenoble, 2000.
17. T. Dang, C. Le Guernic, and O. Maler. Computing reachable states for nonlinear biological models. In Computational Methods in Systems Biology, LNCS 5688, pages 126-141. Springer, 2009.
18. T. Dang, O. Maler, and R. Testylier. Accurate hybridization of nonlinear systems. In Hybrid Systems: Computation and Control, pages 11-19, 2010.
19. G. Frehse. PHAVer: Algorithmic verification of hybrid systems past HyTech. International Journal on Software Tools for Technology Transfer, 10: 263-279, 2008.
20. A. Girard. Reachability of uncertain linear systems using zonotopes. In Hybrid Systems: Computation and Control, LNCS 3414, pages 291-305. Springer, 2005.
21. 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.
22. 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.
23. A. Girard and G. J. Pappas. Verification using simulation. In Hybrid Systems: Computation and Control, LNCS 3927, pages 272-286. Springer, 2006.
24. 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.
25. J. Hoefkens, M. Berz, and K. Makino. Scientific Computing, Validated Numerics, Interval Methods, chapter Verified High-Order Integration of DAEs and Higher-Order ODEs, pages 281-292. Springer, 2001.
26. L. Jaulin, M. Kieffer, and O. Didrit. Applied Interval Analysis. Springer, 2006.
27. A. A. Julius, G. E. Fainekos, M. Anand, I. Lee, and G. J. Pappas. Robust test generation and coverage for hybrid systems. In Hybrid Systems: Computation and Control, LNCS 4416, pages 329-342. Springer, 2007.
28. M. Kloetzer and C. Belta. Reachability analysis of multi-affine systems. In Hybrid Systems: Computation and Control, LNCS 3927, pages 348-362. Springer, 2006.
29. A. B. Kurzhanski and P. Varaiya. Ellipsoidal techniques for reachability analysis. In Hybrid Systems: Computation and Control, LNCS 1790, pages 202-214. Springer, 2000.
30. K. Makino and M. Berz. Rigorous integration of flows and ODEs using Taylor models. In Proc. of Symbolic-Numeric Computation, pages 79-84, 2009.
31. 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.
32. M. Neher, K. R. Jackson, and N. S. Nedialkov. On Taylor model based integration of ODEs. SIAM Journal on Numerical Analysis, 45(1): 236-262, 2007.
33. A. Platzer. Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics. Springer, 2010. ISBN 978-3-642-14508-7.
34. S. Prajna. Barrier certificates for nonlinear model validation. Automatica, 42(1): 117-126, 2006.
35. S. Ratschan and Z. She. Constraints for continuous reachability in the verification of hybrid systems. In Proc. of Artificial Intelligence and Symbolic Computation, LNCS 4120, pages 196-210. Springer, 2006.
36. S. M. Rump. Developments in Reliable Computing, chapter INTLAB - INTerval LABoratory, pages 77-104. Kluwer Academic Publishers, 1999.
37. S. Sankaranarayanan. Automatic abstraction of non-linear systems using change of bases transformations. In Hybrid Systems: Computation and Control, pages 143-152, 2011.
38. S. Sankaranarayanan and G. Fainekos. Falsification of temporal properties of hybrid systems using the cross-entropy method. In Hybrid Systems: Computation and Control, pages 125-134, 2012.
39. 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.