Continuity and computability of reachable sets

Theoretical Computer Science

Volumn 341, Issue 1-3, 2005, Pages 162-195

  Collins, Pieter ^a  

^a CWI   (Netherlands)

Author keywords

Approximation representation; Computable analysis; Computable topological space; Reachable set; Semicontinuous function

Indexed keywords

APPROXIMATION THEORY; COMPUTATION THEORY; CONFORMAL MAPPING; CONTROL SYSTEM ANALYSIS; MATHEMATICAL MODELS; TOPOLOGY; TURING MACHINES;

APPROXIMATION REPRESENTATION; COMPUTABLE ANALYSIS; COMPUTABLE TOPOLOGICAL SPACE; REACHABLE SETS; SEMICONTINUOUS FUNCTION;

SET THEORY;

EID: 23844462483     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2005.05.001     Document Type: Article

References (27)

1. E. Asarin, A. Bouajjani, Perturbed turing machines and hybrid systems, in: Proc. Sixteenth Annu. IEEE Symp. on Logic in Computer Science, IEEE, 2001.
2. E. Asarin, T. Dang, O. Maler, d/dt: a verification tool for hybrid systems, in: Proc. 40th IEEE Conf. on Decision and Control, IEEE Press, New York, 2001.
3. E. Asarin, O. Maler, and A. Pnueli Reachability analysis of dynamical systems having piecewise-constant derivatives Theoret. Comput. Sci. 138 1 1995 35 65
4. J.-P. Aubin Viability theory, Systems & Control: Foundations & Applications 1991 Birkhäuser Boston
5. J.-P. Aubin, and H. Frankowska Set-valued analysis, Systems & Control: Foundations & Applications 1990 Birkhäuser Boston
6. E. Bishop, D. Bridges, Constructive analysis, in: Grundlehren der Mathematischen Wissenschaften Springer, Berlin, Vol. 279 1985 (Fundamental Principles of Mathematical Sciences).
7. V. Brattka Computability over topological structures S.B. Cooper S.S. Goncharov Computability and Models Univ. Ser. Math. 2003 Kluwer/Plenum New York 93 136
8. V. Brattka, Plottable real number functions, in: RNC'5 Real Numbers and Computers, Lyon, France, 2003, pp. 13-30.
9. V. Brattka, and G. Presser Computability on subsets of metric spaces Theoret. Comp. Sci. 305 2003 43 76
10. V. Brattka, and K. Weihrauch Computability on subsets of Euclidean space. I. Closed and compact subsets Theoret. Comput. Sci. 219 1-2 1999 65 93 computability and complexity in analysis (Castle Dagstuhl, 1997)
11. P. Cardaliaguet, M. Quincampoix, and P. Saint-Pierre Set-valued numerical analysis for optimal control and differential games Stochastic and Differential Games, no. 4 Annu. Internat. Soc. Dynam. Games 1999 Birkhäuser Boston 177 247
12. C. Conley, Isolated Invariant Sets and the Morse Index, CBMS Regional Conf. Ser. in Mathematics, Vol. 38, American Mathematical Society, Providence, RI, 1978.
13. M. Dellnitz, G. Froyland, and O. Junge The algorithms behind GAIO-set oriented numerical methods for dynamical systems B. Fiedler Ergodic Theory Analysis and Efficient Simulation of Dynamical Systems 2001 Springer Berlin 145 174 805-807
14. M. Fräzle, Analysis of hybrid systems: An ounce of realism can save an infinity of states, in: J. Flum, M. Rodriguez-Artalejo (Eds.), Computer Science Logic, Lecture Notes in Computer Science, Vol. 1683, Springer, Berlin, Heidelberg, New York, 1999.
15. M. Fräzle, What will be eventually true of polynomial hybrid automata, in: N. Kobayashi, B. C. Pierce (Eds.), Theoretical Aspects of Computer Software, Lecture Notes in Computer Science, Vol. 2215, Springer, Berlin, Heidelberg, New York, 2001, pp. 340-359.
16. E. Klein, and A.C. Thompson Theory of correspondences. Including applications to mathematical economics Canadian Mathematical Society Series of Monographs and Advanced Texts 1984 Wiley New York
17. A.B. Kurzhanski, and István Vályi Ellipsoidal calculus for estimation and control, Systems & Control: Foundations & Applications 1997 Birkhäuser Boston, MA
18. A.B. Kurzhanski, and P. Varaiya On ellipsoidal techniques for reachability analysis. I. External approximations Optim. Methods Softw. 17 2 2002 177 206
19. A.B. Kurzhanski, and P. Varaiya On ellipsoidal techniques for reachability analysis. II. Internal approximations box-valued constraints Optim. Methods Softw. 17 2 2002 207 237
20. Z. Manna, and A. Pnueli The temporal logic of reactive and concurrent systems, Specification 1992 Springer New York
21. K. Mischaikow, M. Mrozek, Conley index., in: Handbook of Dynamical Systems, Vol. 2, North-Holland, Amsterdam, 2002, pp. 393-460.
22. J.R. Munkres Topology: a First Course 1975 Prentice-Hall, Inc. Englewood Cliffs, NJ
23. A. Puri, P. Varaiya, V. Borkar, Epsilon-approximation of differential inclusions, in: R. Alur, T. A. Henzinger, E.D. Sontag (Eds.), Hybrid Systems III, Lecture Notes in Computer Science, Vol. 1066, Springer, Berlin, 1996, pp. 362-376.
24. M. Schröder, A natural weak limit space with admissible representation which is not a limit space, Electr. Notes Theor. Comput. Sci. 66(1).
25. D. Szolnoki Set oriented methods for computing reachable sets and control sets Discrete Contin. Dyn. Syst. Ser. B 3 3 2003 361 382
26. K. Weihrauch Computable analysis - an introduction, Texts in Theoretical Computer Science 2000 Springer Berlin
27. M. Ziegler Computable operators on regular sets MLQ Math. Log. Q. 50 4-5 2004 392 404