Compositional safety analysis using barrier certificates

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

Volumn , Issue , 2012, Pages 15-23

  Sloth, Christoffer ^a   Pappas, George J ^b   Wisniewski, Rafael ^a  

^a AALBORG UNIVERSITY   (Denmark)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Compositionality; Dynamical systems; Reachable sets; Safety analysis; Sum of squares

Indexed keywords

BARRIER CERTIFICATES; COMPOSITIONAL METHOD; COMPOSITIONALITY; EMERGENCY SHUTDOWN; HIGHER-DIMENSIONAL SYSTEMS; REACHABLE SET; SAFETY ANALYSIS; SAFETY VERIFICATION; SUB-PROBLEMS; SUM OF SQUARES; SUM-OF-SQUARES PROGRAMMING; VERIFICATION PROBLEMS;

DYNAMICAL SYSTEMS; HYBRID SYSTEMS;

SAFETY ENGINEERING;

EID: 84860624019     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2185632.2185639     Document Type: Conference Paper

References (16)

1. A. Abate, A. Tiwari, and S. Sastry. Box invariance in biologically-inspired dynamical systems. Automatica, 45(7):1601-1610, 2009.
2. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory, volume 15 of SIAM studies in applied mathematics. SIAM, 1994.
3. S. Boyd, L. Xiao, A. Mutapcic, and J. Mattingley. Notes on decomposition methods, 2008.
4. A. Girard and G. Pappas. Verification using simulation. In J. Hespanha and A. Tiwari, editors, Hybrid Systems: Computation and Control, volume 3927 of Lecture Notes in Computer Science, pages 272-286. Springer Berlin/Heidelberg, 2006. (Pubitemid 44019593)
5. H. Gúeguen, M.-A. Lefebvre, J. Zaytoon, and O. Nasri. Safety verification and reachability analysis for hybrid systems. Annual Reviews in Control, 33(1):25-36, 2009.
6. J. Helton and O. Merino. Coordinate optimization for bi-convex matrix inequalities. In Proceedings of the 36th IEEE Conference on Decision and Control, pages 3609-3613, December 1997.
7. T. Iwasaki. The dual iteration for fixed-order control. IEEE Transactions on Automatic Control, 44(4):783-788, April 1999.
8. J. Laks, L. Pao, and A. Wright. Control of wind turbines: Past, present, and future. In American Control Conference, pages 2096-2103, June 2009.
9. I. Mitchell, A. Bayen, and C. Tomlin. A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games. IEEE Transactions on Automatic Control, 50(7):947-957, 2005. (Pubitemid 41078397)
10. P. A. Parrilo. Semidefinite programming relaxations for semialgebraic problems. Mathematical Programming, 96(2):293-320, 2003. (Pubitemid 44757842)
11. B. T. Polyak. Subgradient methods: A survey of Soviet research. In Proceedings of a IIASA Workshop, volume 3 of Nonsmooth Optimization, pages 5-29, 1977.
12. S. Prajna and A. Jadbabaie. Safety verification of hybrid systems using barrier certificates. In Hybrid Systems: Computation and Control, volume 2993 of Lecture Notes in Computer Science, pages 271-274. Springer Berlin/Heidelberg, 2004.
13. S. Prajna, A. Jadbabaie, and G. J. Pappas. A framework for worst-case and stochastic safety verification using barrier certificates. IEEE Transactions on Automatic Control, 52(8):1415-1428, August 2007. (Pubitemid 47316689)
14. S. Prajna, A. Papachristodoulou, P. Seiler, and P. A. Parrilo. SOSTOOLS and its control applications. In Positive Polynomials in Control, volume 312 of Lecture Notes in Control and Information Sciences, pages 273-292. Springer Berlin/Heidelberg, 2005. (Pubitemid 40171280)
15. N. Z. Shor, K. C. Kiwiel, and A. Ruszcaỳnski. Minimization methods for non-differentiable functions. Springer-Verlag New York, Inc., New York, NY, USA, 1985.
16. U. Topcu, A. Packard, and R. Murray. Compositional stability analysis based on dual decomposition. In Proceedings of the 48th IEEE Conference on Decision and Control, pages 1175-1180, December 2009.