Symbolic models for nonlinear control systems: Alternating approximate bisimulations

SIAM Journal on Control and Optimization

Volumn 48, Issue 2, 2009, Pages 719-733

  Pola, Giordano ^a   Tabuada, Paulo ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Alternating bisimulation; Approximate bisimulation; Incremental stability; Nonlinear systems; Symbolic models

Indexed keywords

ALGORITHMIC GAME THEORIES; ALTERNATING BISIMULATION; APPROXIMATE BISIMULATION; BISIMULATIONS; CONTINUOUS STATE; CONTINUOUS SYSTEMS; CONTROLLER SYNTHESIS; GLOBALLY ASYMPTOTICALLY STABLES; IN CONTROLS; INCREMENTAL STABILITY; SUPERVISORY CONTROLS; SYMBOLIC MODELS;

CONTROL SYSTEM ANALYSIS; FAULT TOLERANCE; GAME THEORY; QUALITY ASSURANCE; SYSTEM STABILITY;

NONLINEAR CONTROL SYSTEMS;

EID: 60649088883     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/070698580     Document Type: Article

References (34)

1. R. ALUR, C. COURCOUBETIS, T. A. HENZINGER, AND P. H. HO, Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems, in Hybrid Systems, Lecture Notes in Comput. Sci. 736, Springer, Berlin, 1993, pp. 209-229.
2. R. ALUR AND D. L. DILL, Automata for modeling real-time systems, in Automata, Languages and Programming, Lecture Notes in Comput. Sci. 443, Springer, Berlin, 1990, pp. 322-335.
3. R. ALUR, T. HENZINGER, O. KUPFERMAN, AND M. VARDI, Alternating refinement relations, in Proceedings of the 8th International Conference on Concurrence Theory, Lecture Notes in Comput. Sci. 1466, Springer, Berlin, 1998, pp. 163-178.
4. D. ANGELI, A Lyapunov approach to incremental stability properties, IEEE Trans. Automat. Control, 47 (2002), pp. 410-421.
5. D. ANGELI AND E. D. SONTAG, Forward completeness, unboundedness observability, and their Lyapunov characterizations, Systems Control Lett., 38 (1999), pp. 209-217.
6. A. ARNOLD, A. VINCENT, AND I. WALUKIEWICZ, Games for synthesis of controllers with partial observation, Theoret. Comput. Sci., 303 (2003), pp. 7-34.
7. P. E. CAINES AND Y. J. WEI, Hierarchical hybrid control systems: A lattice-theoretic formulation, Special Issue on Hybrid Systems, IEEE Trans. Automat. Control, 43 (1998), pp. 501-508.
8. M. B. EGERSTEDT, E. FRAZZOLI, AND G. J. PAPPAS, EDS., Special Issue on Symbolic Methods for Complex Control Systems, IEEE Trans. Automat. Control 51, (2006).
9. D. FORSTNER, M. JUNG, AND J. LUNZE, A discrete-event model of asynchronous quantised systems, Automatica J. IFAC, 38 (2002), pp. 1277-1286.
10. A. GLRARD, Approximately bisimilar finite abstractions of stable linear systems, in Hybrid Systems: Computation and Control, Lecture Notes in Comput. Sci. 4416, A. Bemporad, A. Bicchi, and G. Buttazzo, eds., Springer, Berlin, 2007, pp. 231-244.
11. A. GIRARD AND G. J. PAPPAS, Approximation metrics for discrete and continuous systems, IEEE Trans. Automat. Control, 52 (2007), pp. 782-798.
12. T. A. HENZINGER, P. W. KOPKE, A. PURI, AND P. VARAIYA, What's decidable about hybrid automata?, J. Comput. System Sci., 57 (1998), pp. 94-124.
13. T. A. HENZINGER, R. MAJUMDAR, AND V. PRABHU, Quantifying similarities between timed systems, in Proceedings of the Third International Conference on Formal Modeling and Analysis of Timed Systems, 2005, Lecture Notes in Comput. Sci. 3829, Springer, Berlin, 2005, pp. 226-241.
14. R. ISAACS, Differential Games, Dover, New York, 1999.
15. X. D. KOUTSOUKOS, P. J. ANTSAKLIS, J. A. STIVER, AND M. D. LEMMON, Supervisory control of hybrid systems, in Proceedings of the IEEE, 88 (2000), pp. 1026-1049.
16. E. B. LEE AND L. MARKUS, Foundations of Optimal Control Theory, SIAM Series in Applied Mathematics, John Wiley and Sons, New York, 1967.
17. G. LAFFERRIERE, G. J. PAPPAS, AND S. SASTRY, O-minimal hybrid systems, Math. Control Signals Systems, 13 (2000), pp. 1-21.
18. Y. LIN, E. P. SONTAG, AND Y. WANG, A smooth converse Lyapunov theorem for robust stability, SIAM J. Control Optim., 34 (1996), pp. 124-160.
19. R. MILNER, Communication and Concurrency, Prentice-Hall, Englewood Cliffs, NJ, 1989.
20. T. MOOR, J. RAISCH, AND S. D. O'YOUNG, Discrete supervisory control of hybrid systems based on l-complete approximations, J. Discrete Event Dyn. Syst., 12 (2002), pp. 83-107.
21. X. NICOLLIN, A. OLIVERO, J. SIFAKIS, AND S. YOVINE. An approach to the description and analysis of hybrid systems, in Hybrid Systems, Lecture Notes in Comput. Sci. 736, Springer, Berlin, 1993, pp. 149-178.
22. D. M. R. PARK, Concurrency and automata on infinite sequences, in Proceedings of the 5th GI Conference on Theoretical Computer Science, Lecture Notes in Comput. Sci. 104, Springer, London, 1981, pp. 167-183.
23. G. POLA, A. GIRARD, AND P. TABUADA, Approximately bisimilar symbolic models for nonlinear control systems, Automatica, 44 (2008), pp. 2508-2516.
24. G. POLA AND P. TABUADA, Symbolic models for linear control systems with disturbances, in Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, 2007, pp. 4643-4647.
25. G. POLA AND P. TABUADA, Symbolic models for nonlinear control systems affected by disturbances, in 47th IEEE Conference on Decision and Control, Cancun, Mexico, 2008, pp. 251-256.
26. A. PURI AND P. VARAIYA, Decidability of hybrid systems with rectangular differential inclusion, in Proceedings of the 6th International Conference on Computer Aided Verification (CAV '94), Lecture Notes in Comput. Sci. 818, Springer, London, 1994, pp. 95-104.
27. P. J. RAMADGE AND W. M. WONHAM, Supervisory control of a class of discrete event systems, SIAM J. Control Optim., 25 (1987), pp. 206-230.
28. R. R. STOLL, Sci Theory and Logic, W. H. Freeman, San Francisco, 1963.
29. P. TABUADA, Symbolic models for control systems, Acta Inform., 43 (2007), pp. 477-500.
30. P. TABUADA, An approximate simulation approach to symbolic control, IEEE Trans. Automat. Control, 53 (2008), pp. 1406-1418.
31. P. TABUADA AND G. J. PAPPAS, Linear time logic control of discrete-time linear systems, IEEE Trans. Automat. Control, 51 (2006), pp. 1862-1877.
32. A. J. VAN DER SCHAFT, Equivalence of dynamical systems by bisimulation, IEEE Trans. Automat. Control, 49 (2004), pp. 2160-2172.
33. M. YING AND M. WIRSING, Approximate bisimilarity, in Algebraic Methodology and Software Technology, Lecture Notes in Comput. Sci. 1816, Springer, Berlin, 2000, pp. 309-322.
34. W. ZIELONKA, Infinite games on finitely coloured graphs with applications to automata on infinite trees, Theoret. Comput. Sci., 200 (1998), pp. 135-183.