Computation of discrete abstractions of arbitrary memory span for nonlinear sampled systems

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5469, Issue , 2009, Pages 306-320

  Reibig, Gunther ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CONVEX HULL; DISCRETE ABSTRACTION; HALF SPACES; HALF-SPACE; LEVEL SET; MEMORY SPAN; NUMERICAL INTEGRATIONS; QUANTIZER; REACHABLE SET; SAMPLING INTERVAL; SAMPLING PERIOD; SMOOTH SYSTEM; STABILITY PROPERTIES;

ABSTRACTING; ELECTRIC GROUNDING; HYBRID COMPUTERS; HYBRID SYSTEMS; INITIAL VALUE PROBLEMS; ORDINARY DIFFERENTIAL EQUATIONS; STABILITY; SYSTEMS ANALYSIS;

SET THEORY;

EID: 67650164753     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-00602-9_22     Document Type: Conference Paper

References (34)

1. Willems, J.C.: Models for dynamics. In: Dynam. Report. Ser. Dynam. Systems Appl., vol. 2, pp. 171-269. Wiley, Chichester (1989)
2. Willems, J.C.: Paradigms and puzzles in the theory of dynamical systems. IEEE Trans. Automat. Control 36(3), 259-294 (1991)
3. Blanke, M., Kinnaert, M., Lunze, J., Staroswiecki, M.: Diagnosis and fault-tolerant control. Springer, Berlin (2003)
4. Tomlin, C.J., Mitchell, I., Bayen, A.M., Oishi, M.: Computational techniques for the verification of hybrid systems. Proc. IEEE 91(7), 986-1001 (2003) (Pubitemid 40890836)
5. Koutsoukos, X.D., Antsaklis, P.J., Stiver, J.A., Lemmon, M.D.: Supervisory control of hybrid systems. Proc. IEEE 88(7), 1026-1049 (2000)
6. Moor, T., Raisch, J.: Supervisory control of hybrid systems within a behavioural framework. Systems Control Lett. 38(3), 157-166 (1999) (Pubitemid 129608448)
7. Moor, T., Davoren, J.M., Anderson, B.D.O.: Robust hybrid control from a behavioural perspective. In: Proc. 41th IEEE Conference on Decision and Control, Las Vegas, U.S.A., 2002, pp. 1169-1174. IEEE, New York (2002)
8. Gr̈une, L., Junge, O.: Approximately optimal nonlinear stabilization with preservation of the Lyapunov function property. In: Proc. 46th IEEE Conference on Decision and Control, New Orleans, Louisiana, U.S.A., 2007, pp. 702-707. IEEE, New York (2007) (Pubitemid 351277235)
9. Ramadge, P.J., Wonham, W.M.: Modular feedback logic for discrete event systems. SIAM J. Control Optim. 25(5), 1202-1218 (1987)
10. Ramadge, P.J.G., Wonham, W.M.: The control of discrete event systems. Proc. IEEE 77(1), 81-98 (1989)
11. Gallo, G., Longo, G., Pallottino, S., Nguyen, S.: Directed hypergraphs and applications. Discrete Appl. Math. 42(2-3), 177-201 (1993)
12. Kurzhanski, A.B., Varaiya, P.: Ellipsoidal techniques for reachability analysis. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 202-214. Springer, Heidelberg (2000)
13. Moor, T., Raisch, J.: Abstraction based supervisory controller synthesis for high order monotone continuous systems. In: Engell, S., Frehse, G., Schnieder, E. (eds.) Modelling, Analysis, and Design of Hybrid Systems. Lect. Notes Control Inform. Sciences, vol. 279, pp. 247-265. Springer, Heidelberg (2002)
14. Junge, O.: Rigorous discretization of subdivision techniques. In: International Conference on Differential Equations, Berlin, 1999, vol. 1, 2, pp. 916-918. World Sci. Publ., River Edge (2000)
15. Puri, A., Varaiya, P., Borkar, V.: ε-approximation of differential inclusions. In: Proceedings of the 34th IEEE Conference on Decision and Control, New Orleans, LA, U.S.A., December 13-15, 1995, vol. 3, pp. 2892-2897. IEEE, Los Alamitos (1995)
16. Chutinan, A., Krogh, B.H.: Computational techniques for hybrid system verification. IEEE Trans. Automat. Control 48(1), 64-75 (2003)
17. Geist, S., Reißig, G., Raisch, J.: An approach to the computation of reachable sets of nonlinear dynamic systems - an important step in generating discrete abstractions of continuous systems. In: Domek, S., Kaszýnski, R. (eds.) Proc. 11th IEEE Int. Conf. Methods and Models in Automation and Robotics (MMAR), Miedzyzdroje, Poland, August 29-September 1, pp. 101-106 (2005), www.reiszig.de/gunther/pubs/i05MMAR.abs.html
18. Gr̈une, L., M̈uller, F.: Set oriented optimal control using past information. In: Proc. 2008 Math. Th. of Networks and Systems (MTNS), Blacksburg, Virginia, U.S.A, July 28 - August 1 (2008)
19. Tiwari, A.: Abstractions for hybrid systems. Form. Methods Syst. Des. 32(1), 57- 83 (2008); Proc. 7th Intl. Workshop Hybrid Systems: Computation and Control (HSCC), Philadelphia, U.S.A., March 25-27 (2004)
20. Kloetzer, M., Belta, C.: A fully automated framework for control of linear systems from temporal logic specifications. IEEE Trans. Automat. Control 53(1), 287-297 (2008)
21. Tabuada, P.: An approximate simulation approach to symbolic control. IEEE Trans. Automat. Control 53(6), 1406-1418 (2008)
22. Reißig, G.: Convexity of reachable sets of nonlinear ordinary differential equations. Automat. Remote Control 68(9), 1527-1543 (2007); (Russian transl. in Avtomat. i Telemekh. (9), 64-78 (2007), www.reiszig.de/ gunther/pubs/i07Convex.abs.html
23. Reißig, G.: Convexity of reachable sets of nonlinear discrete-time systems. In: Kaszýnski, R. (ed.) Proc. 13th IEEE Int. Conf. Methods and Models in Automation and Robotics (MMAR), Szczecin, Poland, August 27-30, pp. 199-204 (2007), www.reiszig.de/gunther/pubs/i07MMAR.abs.html
24. Hirsch, M.W., Smale, S.: Differential Equations, Dynamical Systems, and Linear Algebra. Pure and Appl. Math., vol. 60. Academic Press, London (1974)
25. Hartman, P.: Ordinary differential equations. Classics in Applied Mathematics, vol. 38. SIAM, Philadelphia (2002)
26. Halin, R.: Graphentheorie, 2nd edn. Wiss. Buchgesellschaft, Darmstadt (1989)
27. Rockafellar, R.T.: Convex analysis. Princeton Mathematical Series, vol. 28. Princeton University Press, Princeton (1970)
28. Reißig, G.: Local fill reduction techniques for sparse symmetric linear systems. Electr. Eng. 89(8), 639-652 (2007), www.reiszig.de/gunther/pubs/ i06Fill.abs.html (Pubitemid 47333746)
29. Reißig, G.: Fill reduction techniques for circuit simulation. Electr. Eng. 90(2), 143-146 (2007), www.reiszig.de/gunther/pubs/i07Fill.abs.html (Pubitemid 350205960)
30. Zampieri, G., Gorni, G.: Local homeo- and diffeomorphisms: invertibility and convex image. Bull. Austral. Math. Soc. 49(3), 377-398 (1994)
31. Polyak, B.T.: Convexity of nonlinear image of a small ball with applications to optimization. Set-Valued Anal. 9(1-2), 159-168 (2001)
32. Bobylev, N.A., Emeĺyanov, S.V., Korovin, S.K.: Convexity of images of convex sets under smooth maps. Nelineinaya Dinamika i Upravlenie (2), 23-32 (2002); Russian. Engl. transl. in Comput. Math. Model. 15(3), 213-222 (Pubitemid 38990637)
33. Wolfram, S.: The Mathematica ® book, 5th edn. Wolfram Media, Inc., Champaign (2003)
34. von Lossow, M.: A min-max version of Dijkstra's algorithm with application to perturbed optimal control problems. In: Proceedings in Applied Mathematics and Mechanics ICIAM 2007/GAMM 2007, Z̈urich, Schweiz, vol. 7 (2007)