Symbolic control of linear systems based on symbolic subsystems

IEEE Transactions on Automatic Control

Volumn 51, Issue 6, 2006, Pages 1003-1013

  Tabuada, Paulo ^a  

^a University of Notre Dame   (United States)

Author keywords

Bisimulation; Simulation; Symbolic control; Symbolic subsystems

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; CONTROL EQUIPMENT; CONTROL SYSTEM SYNTHESIS; FEEDBACK CONTROL;

BISIMULATION; SYMBOLIC CONTROL; SYMBOLIC SUBSYSTEMS;

LINEAR CONTROL SYSTEMS;

EID: 33745728854     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2006.876946     Document Type: Article

References (54)

1. R. Alur, C. Courcoubetis, N. Halbwachs, T. A. Henzinger, P. H. Ho, X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine, "Hybrid automata: An algorithmic approach to specification and verification of hybrid systems " Theoret. Comput. Sci., vol. 138, pp. 3-34, 1995.
2. R. Alur and D. L. Dill, "A theory of timed automata," Theoret. Comput. Sci., vol. 126, pp. 183-235, 1994.
3. D. Angeli, "A lyapunov approach to incremental stability properties," IEEE Trans. Autom. Control, vol. 47, no. 3, pp. 410-421, MAr. 2002.
4. P. J. Antsaklis, J. A. Stiver, and M. D. Lemmon, "Hybrid system modeling and autonomous control systems," in Hybrid Systems, R. L. Grossman, A. Nerode, A. P. Ravn, and H. Rischel, Eds. New York: Springer-Verlag, 1993, vol. 736, Lecture papers in Computer Sience, pp. 366-392.
5. A. Arnold, A. Vincent, and I. Walukiewicz, "Games for synthesis of controllers with partial observation," Theoret. Comput. Sci., vol. 28, no. 1, pp. 7-34, 2003.
6. A. Bicchi, A. Marigo, and B. Piccoli, "On the rechability of quantized control systems," IEEE Trans. Autom. Control, vol. 47, no. 4, pp. 546-563, Apr. 2002.
7. T. Brihaye, C. Michaux, C. Riviére, and C. Troestler, "On o-minimal hybrid systems," in Hybrid Systems: Computation and Control, R. Alur and G. J. Pappas, Eds. New York: Springer-Verlag, 2004, vol. 2993, Lecture papers in Computer Science, pp. 219-233.
8. M. Broucke, "A geometric approach to bisimulation and verification of hybrid systems," in Hybrid Systems: Computation and Control, F. W. Vaandrager and J. H. van Schuppen, Eds. New York: Springer-Verlag, 1999, vol. 1569, Lecture papers in Computer Science, pp. 61-75.
9. A. Chotinan and B. H. Krogh, "Verification of infinite state dynamical systems using approximate quotient transition systems," IEEE Trans. Autom. Control, vol. 46,no. 9, pp. 1401-1410, Sep. 2001.
10. C. Cassandras and S. Lafortune, Introduction to Discrete Event Sysems. Boston, MA: Kluwer, 1999.
11. E. M. M. Clarke, D. Peled, and O. Grumberg, Model Checking. Cambridge, MA: MIT Press, 1999.
12. P. E. Caines and Y. J. Wei, "Hierarchical hybrid control systems: A lattice theoretic formulation," IEEE Trans. Autom. Control, vol. 43, no. 4, pp. 501-508, Apr. 1998.
13. L. de Alfaro, T. A. Henzinger, and R. Majumdar, "Symbolic algorithms for infinite-state games," in Proc. CONCUR 01: Concurrency Theory, l2th Int. Conf., 2001, vol. 2154, Lecture papers in Computer Science.
14. J. M. Davoren, T. Moor, and A. Nerode, "Hybrid control loops, A/D maps and dynamic specifications," in Hybrid Systems: Computation and Control, C. Tomlin and M. R. Greenstreet, Eds. New York: Springer-Verlag, 2002, vol. 2289, Lecture papers in Computer Sience.
15. M. Egerstedt and R. W. Brockett, "Feedback can reduce the specification complexity of motor programs," IEEE Trans. Autom. Control, vol. 48, no. 2, pp. 213-223, Feb. 2003.
16. E. Frazzoli, M. A. Dahleh, and E. Feron, "A maneuver-based hybrid control architecture for autonomous vehicle motion planning," in Software Enabled Control: Information Technology for Dynamical Systems, G. Balas and T. Samad, Eds. New York: IEEE Press, 2003.
17. A. Girard and G. J. Pappas, "Approximate bisimulations for nonlinear dynamical systems," in Proc. 44th IEEE Conf. Decision and Control, Seville, Spain, 2005, pp. 684-689.
18. T. A. Henzinger, P. W. Kopke, A. Puri, and P. Varaiya, "What's decidable about hybrid automata?," J. Comput. Syst. Sci., vol. 57, pp. 94-124, 1998.
19. T. A. Henzinger and R. Majumdar, "Symbolic model checking for rectangular hybrid systems," in TACAS 2000: Tools and Algorithms for the Construction and Analysis of Systems, S. Graf, Ed. New York: Springer-Verlag, 2000, Lecture papers in Computer Science.
20. T. A. Henzinger, R. Majumdar, and J.-F. Raskin, "A classification of symbolic transition systems," ACM Trans. Comput. Logic, pp. 1-31, 2003.
21. E. Haghverdi, P. Tabuada, and G. J. Pappas, "Bisimulation relations for dynamical, control and hybrid systems," Theoret. Comput. Sci., vol. 34, no. 2-3, pp. 387-392, 2005.
22. J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages and Computation. Reading, MA: Addison-Wesley, 1979.
23. D. Hristu-Varsakelis, M. Egerstedt, and P. S. Krishnaprasad, "On the structural complexity of the motion description language mdle," in Proc. 42nd IEEE Conf. Decision and Control, Maui, HL 2003, pp. 3360-3365.
24. X. Koutsoukos and P. Antsaklis, "Safety and reachability of piecewise linear hybrid dynamical systems based on discrete abstractions," J. Discrete Event Dyna. Syst.: Theory Appl., vol. 13, no. 3, pp. 203-243, 2003.
25. R. Kumar and V. K. Garg, Modeling and Control of Logical Discrete Event Systems. Norwell, MA: Kluwer, 1995.
26. O. Kupferman, P. Madhusudan, P. S. Thiagarajan, and M. Y. Vardi, "Open systems in reactive environments: Control and synthesis," Proc. 11th Int. Conf. Concurency Theory vol. 1877, Lecture papers in Computer Science, pp. 92-107. New York, Springer-Verlag, 2000.
27. T. J. Koo, G. J. Pappas, and S. Sastry, "Mode switching synthesis for reachability specifications," in Hybrid Systems: Computation and Control, M. D. Di Benedetto and A. Sangiovanni-Vincentelli, Eds. New York: Springer-Verlag, 2001, vol. 2034, Lecture papers in Computer Science, pp. 333-346.
28. G. Lafferriere, G. J. Pappas, and S. Sastry, "Ominimal hybrid systems," Math. Control, Signals Syst., vol. 13, no. 1, pp. 1-21, March 2000.
29. J. Lunze, "Qualitative modelling of linear dynamical systems with quantized state measurements," Automatica, vol. 30, pp. 417-431, 1994.
30. J. O. Moody and P. J. Antsaklis, Supervisory Control of Discrete Event Systems Using Petri Nets. Norwell, MA: Kluwer, 1998.
31. R. Milner, Communication and Concurrency. Englewood Cliffs, NJ: Prentice-Hall, 1989.
32. T. Moor, J. Raisch, and S. D. O'Young, "Discrete supervisory control of hybrid systems based on 1-complete approximations," J. Discrete Event Dyna. Syst., vol. 12, no. 1, pp. 83-107, 2002.
33. P. Madhusudan and P. S. Thiagarajan, "Branching time controllers for discrete event systems," Theoret. Comput. Sci., vol. 274, pp. 117-149, Mar. 2002.
34. A. Nerode and W. Kohn, "Models for hybrid systems: Automata, topologies, controllability, observability," in Hybrid Systems, R. L. Grossman, A. Nerode, A. P. Ravn, and H. Rischel, Eds. New York: Springer-Verlag, 1993, vol. 736, Lecture papers in Computer Sience, pp. 317-356.
35. G. J. Pappas, "Bisimilar linear systems," Automatica, vol. 39, no. 12, pp. 2035-2047, Dec. 2003.
36. D. M. R. Park, Concurrency and Automata on Infinite Sequences vol. 104, Lecture papers in Computer Science, pp. 167-183, 1981.
37. S. Pancanti, L. Leonardi, L. Pallottino, and A. Bicchi, "Optimal control of quantized linear systems," in Hybrid Systems: Computation and Control, C. Tomlin and M. R. Greenstreet, Eds. New York: Springer-Verlag, 2002, Lecture papers in Computer Sience, pp. 351-363.
38. A. Puri and P. Varaiya, "Decidability of hybrid systems with rectangular inclusions," in Computer Aided Verification. Stanford, CA: Springer-Verlag, 1994, pp. 95-104.
39. G. Pola, A. J. van der Schaft, and M. D. di Benedetto, "Bisimulation theory for switching linear systems," in Proc. 43rd IEEE Conf. Decision and Control, Paradise Island, Bahamas, 2004, pp. 1406-1411.
40. J. Raisch and S. D. O'Young, "Discrete approximations and supervisory control of continuous systems," IEEE Trans. Autom. Control, vol. 43, no. 4, pp. 569-573, Apr. 1998.
41. J. A. Stiver, X. D. Koutsoukos, and P. J. Antsaklis, "An invariant based approach to the design of hybrid control systems," Int. J. Robust Nonlinear Control, vol. 11, no. 5, pp. 453-478, 2001.
42. O. Stursberg, S. Kowalewski, I. Hoffman, and J. Preussig, "Comparing timed and hybrid automata as approximations of continuous systems," in Hybrid Systems IV, P. J. Antsaklis, W. Kohn, A. Nerode, and S. Sastry, Eds. New York: Springer-Verlag, 1997, vol. 1273, Lecture papers in Computer Science, pp. 361-377.
43. P. Tabuada, "Flatness and finite bisimulations in discrete time," in Proc. l6th Int. Symp. Mathematical Theory of Networks and Systems, Leuven, Belgium, Jul. 2004.
44. P. Tabuada, "Open maps, alternating simulations and controller synthesis," in P. Gardner and N. Yoshida, Eds., Proc. l5th Int. Conf. Concurrence Theory vol. 3170, Lecture papers in Computer Science, pp. 466-480 London, UK, Springer, 2004.
45. W. Thomas, "On the synthesis of strategies in infinite games," Proc. l2th Annu. Symposium on Theoretical Aspects of Computer Science vol. 900, Lecture papers in Computer Science, pp. 1-13. New York, Springer-Verlag, 1995.
46. A. Tiwari and G. Khanna, "Series of abstractions for hybrid automata," in Hybrid Systems: Computation and Control, C. Tomlin and M. R. Greenstreet, Eds. New York: Springer-Verlag, 2002, vol. 2289, Lecture papers in Computer Science, pp. 465-478.
47. D. C. Tarraf, A. Megretski, and M. A. Dahleh, "Finite automata approximations with error bounds for systems with quantized actuation and measurement: A case study," in Proc. 43rd IEEE Conf. Decision and Control, Paradise Island, Bahamas, 2004, pp. 1436-1441.
48. P. Tabuada and G. J. Pappas, "Linear time logic control of discrete-time linear systems," IEEE Trans. Autom. Control, 2006, to be published.
49. P. Tabuada and G. J. Pappas, "Finite bisimulations of controllable linear systems," in Proc. 42nd IEEE Conf. Decision and Control, Honolulu, Hawaii, 2003.
50. P. Tabuada and G. J. Pappas, "From discrete specifications to hybrid control," in Proc. 42nd IEEE Conf. Decision and Control, Honolulu, Hawaii, 2003.
51. P. Tabuada and G. J. Pappas, "Model checking LTL over controllable linear systems is decidable," in Hybrid Systems: Computation and ControlO. Maler and A. Pnueli, Eds. New York: Springer-Verlag, 2003, vol. 2623, Lecture papers in Computer Sience.
52. P. Tabuada and G. J. Pappas, "Bisimilar control affine systems," Syst. Control Lett., vol. 52, no. 1, pp. 49-58, 2004.
53. A. J. van der Schaft, "Bisimulation of dynamical systems," in Hybrid Systems: Computation and Control, R. Alur and G. J. Pappas, Eds. New York: Springer-Verlag, 2004, vol. 2993, Lecture papers in Computer Science, pp. 555-569.
54. R. Vidal, S. Schaffert, O. Shakernia, J. Lygeros, and S. Sastry, "Decidable and semi-decidable controller synthesis for classes of discrete time hybrid systems," in Proc. 40th IEEE Con. Decision and Control, Orlando, FL, Dec. 2001, pp. 1243-1248.