Verifying tolerant systems using polynomial approximations

Proceedings - Real-Time Systems Symposium

Volumn , Issue , 2009, Pages 181-190

  Prabhakar, Pavithra ^a   Vladimerou, Vladimeros ^b   Viswanathan, Mahesh ^a   Dullerud, Geir E ^c  

^a University of Illinois at Urbana Champaign   (United States)

^b LUND UNIVERSITY   (Sweden)

^c UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

simulation; Approximation; Hybrid automata; Hybrid systems; Logical characterization

Indexed keywords

AIR TRAFFICS; FIRST ORDER THEORIES; FLOW FUNCTION; HYBRID AUTOMATONS; LOGICAL CHARACTERIZATION; ORIGINAL SYSTEMS; SAFETY VERIFICATION; TECHNICAL TOOLS; VERIFICATION PROCESS;

ELECTRIC GROUNDING; HYBRID COMPUTERS; HYBRID SYSTEMS; REAL TIME SYSTEMS; TRANSLATION (LANGUAGES);

POLYNOMIAL APPROXIMATION;

EID: 77649326306     PISSN: 10528725     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/RTSS.2009.28     Document Type: Conference Paper

References (27)

1. https://netfiles.uiuc.edu/pprabha2/approx.pdf.
2. R. Alur, C. Courcoubetis, N. Halbwachs, T. A. Henzinger, P.-H. Ho, X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine. The algorithmic analysis of hybrid systems. Theoretical Computer Science, 138(1):3-34, 1995.
3. Rajeev Alur and David L. Dill. A theory of timed automata. Theoretical Computer Science, 126(2):183-235, 1994.
4. Eugene Asarin, Oded Maler, and Amir Pnueli. Reachability analysis of dynamical systems having piecewise-constant derivatives. Theoretical Computer Science, 138(1):35-65, 1995.
5. Vincent D. Blondel, Olivier Bournez, Pascal Koiran, Christos H. Papadimitriou, and John N. Tsitsiklis. Deciding stability and mortality of piecewise affine dynamical systems. Theoretical Computer Science, 255(1-2):687-696, 2001.
6. V. K. Dzyadyk. Approximation methods for solutions of differential and integral equations. VSP, Utrecht, The Netherlands, 1995.
7. Lorentz G. G. Bernstein Polynomials. University of Toronto Press, Toronto, 1953.
8. Antoine Girard, A. Agung Julius, and George J. Pappas. Approximate simulation relations for hybrid systems. Discrete Event Dynamic Systems, 18(2):163-179, 2008.
9. Antoine Girard, Giordano Pola, and Paulo Tabuada. Approximately bisimilar symbolic models for incrementally stable switched systems, 2008.
10. 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.
11. Thomas A. Henzinger, Peter W. Kopke, Anuj Puri, and Pravin Varaiya. What's decidable about hybrid automata? In Proc. 27th Annual ACM Symp. on Theory of Computing (STOC), pages 373-382, 1995.
12. G. Lafferriere, G. Pappas, and S. Sastry. O-minimal hybrid systems, 1998.
13. Ruggero Lanotte and Simone Tini. Taylor approximation for hybrid systems. Inf. Comput., 205(11):1575-1607, 2007.
14. Robin Milner. Communication and Concurrency. Prentice-Hall, Inc, 1989.
15. V. Mysore and A. Pnueli. Refining the undecidability frontier of hybrid automata. In Proceedings of the International Conference on the Foundations of Software Technology and Theoretical Computer Science, pages 261-272, 2005.
16. Y. Pang, M. P. Spathopoulos, and Hao Xia. Reachability and optimal control for linear hybrid automata: A quantifier elimination approach. IJC, 80(5):731-748, May 2007.
17. G. Edgar Parker and James S. Sochacki. Implementing the picard iteration. Neural, Parallel, and Scientific Computations, (4):97-112, 1996.
18. Charles Émile Picard. Traite D'Analyse, volume 3. Guthier-Villars, Paris, France, 1922-28.
19. André Platzer and Edmund M. Clarke. Computing differential invariants of hybrid systems as fixedpoints. In ICAV, pages 176-189, 2008.
20. Andreé Platzer and Edmund Clarke. Computing differential invariants of hybrid systems as fixedpoints. Technical Report CMU-CS-08-103, Pittsburg, PA, February 2008.
21. A. Puri, V. Borkar, and P. Varaiya. ε-Approximation of differential inclusions. In Proceedings of HSCC, pages 362-376, 1996.
22. A. Puri, P. Varaiya, and V. Borkar. ε-approximation of differential inclusions. Decision and Control, 1995., Proceedings of the 34th IEEE Conference on, 3:2892-2897 vol.3, Dec 1995.
23. Evgeny Yakovlevich Remez. On the determination of polynomial approximations of a given degree, volume 10. 1934.
24. Walter Rudin. Principles of Mathematical Analysis. McGraw-Hill, 3rd edition, 1976.
25. Bernstein S. Dmonstration du thorme de weierstrass fonde sur le calcul des probabilities. Communications of the Mathematical Society, 13:1-2, 1912.
26. Alfred Tarski. A Decision Method for Elementary Algebra and Geometry. University of California Press, 2nd edition, 1951.
27. V. Vladimerou, P. Prabhakar, M. Viswanathan, and G. E. Dullerud. Stormed hybrid systems. In ICALP Proceedings, Reykjavík, 2008.