Abstract
A fundamental relationship between the controllability of a language with respect to another language and a set of uncontrollable events in the Supervisory Control Theory initiated by (Ramadge and Wonham, 1989) and bisimulation of automata models is derived. The theoretical results relating bisimulation to controllability support an efficient solution to the Basic Supervisory Control Problem. Using (Fernandez, 1990) generalization of the partition refinement algorithm of (Paige and Tarjan, 1987), it is possible to find a partition which represents the supremal controllable sublanguage of an automaton with respect to the language of another automaton and a set of events in a worst-case running time of O( m log(n)), where m is the number of transitions and n is the number of states. Utilizing the bisimulation property of language controllability and derived relationships between automata languages and input/output finite-state machine behaviors, a precise relationship is formally derived between Supervisory Control Theory and the system-theoretic problem posed by (DiBenedetto et al., 1994) called Strong Input/Output FSM Model Matching. Specifically, it is proven that in deterministic settings instances of each problem can be mapped to the other framework and solved.
Similar content being viewed by others
References
Arnold, A. 1994. Finite Transition Systems. NJ: Prentice Hall.
Baeten, J. C. M., and Weijland, W. P. 1990. Process algebra. Cambridge Tracts in Theoretical Computer Science 18.
Barrett, G., and Lafortune, S. 1996. A bisimulation approach to the supervisory control of discrete event systems. Proc. of 34th Annual Allerton Conference on Communication, Control and Computing. Allerton Park, IL.
Barrett, G., and Lafortune, S. 1997. Using bisimulation to solve discrete event control problems. Proc. 1997 American Control Conf. Albuquerque, NM, pp. 2337-2341.
Bloom, B., Istrail, S., and Meyer, A. 1988. Bisimulation can't be traced: Preliminary report. Proc. of 15th Annual SIGACT-SIGPLAN Symposium on Principles of Programming Languages.
Cassandras, C., Lafortune, S., and Olsder, G. 1995. Introduction to the modelling, control and optimization of discrete event systems. Trends in Control. A European Perspective. A. Isidori, ed., Springer-Verlag, pp. 217- 291.
DiBenedetto, M. D., Saldanha, A., and Sangiovanni-Vincentelli, A. 1994. Model matching for finite state machines. Proc. of 33rd Conf. Decision and Control. Lake Buena Vista, FL. pp. 3117-3124.
DiBenedetto, M. D., Saldanha, A., and Sangiovanni-Vincentelli, A. 1995. Strong model matching for finite state machines. Proc. of 3rd European Control Conference. Rome, Italy, pp. 2027-2034.
DiBenedetto, M. D., Saldanha, A., and Sangiovanni-Vincentelli, A. 1995. Strong model matching for finite state machines with non-deterministic reference model. Proc. of 34rd Conf. Decision and Control. New Orleans, LA. pp. 422-426.
DiBenedetto, M. D., Saldanha, A., and Sangiovanni-Vincentelli, A. 1996. Model matching for finite state machines. Cadence Berkeley Laboratories Technical Report.
Fabian, M. 1995. On object oriented nondeterministic supervisory control. Ph.D. thesis, Chalmers University of Technology.
Fernandez, J. 1990. An implementation of an efficient algorithm for bisimulation equivalence. Sci. Comput. Programming 13: 219-236.
Fernandez, J. 1996. Personal communications.
Hadj-Alouane, N. B., Lafortune, S., and Lin, F. 1994. Variable lookahead supervisory control with state information. IEEE Trans. Automat. Contr. 39-12: 2398-2410.
Hayes, J. P. 1993. Introduction to Digital Logic Design. Reading, MA: Addison-Wesley.
Heymann, M., and Lin, F. 1996. Discrete event control of nondeterministic systems. Tech. Report # CIS 9601, Department of Computer Science Technion, Israel Institute of Technology.
Heymann, M., and Meyer, G. 1991. An algebra of discrete event processes. Tech. Report NASA Memorandum 102848. NASA, Ames Research Center, Moffett Field, CA.
Inan, K. 1994. Nondeterministic supervision under partial observation. 11th International Conference on Analysis and Optimization of Systems: Discrete Event Systems. G. Cohen and J. Quadrat, eds., Springer-Verlag, pp. 39- 48.
Kohavi, Z. 1978. Switching and Finite Automata Theory, 2nd ed. New York: McGraw-Hill.
Kumar, R., Garg, V., and Marcus, S. I. On controllability and normality of discrete-event dynamical systems. Syst. Contr. Lett. 17: 157-168.
Overkamp, A. 1997. Supervisory control using failure semantics and partial specifications. IEEE Trans. Automat. Contr. 42-4: 498-510.
Paige, R., and Tarjan, R. 1987. Three partition refinement algorithms. SIAM J. Comput. 16-6: 973-989.
Ramadge, P. J., and Wonham, W. M. 1987. Supervisory control of a class of discrete event processes. SIAM J. Control Optim. 25-1: 206-230.
Ramadge, P. J., and Wonham, W. M. 1989. The control of discrete event systems. Proc. of the IEEE 77-1: 81-98.
Sangiovanni-Vincentelli, A. 1995. Personal communications.
Shayman, M., and Kumar, R. 1995. Supervisory control of nondeterministic systems with driven events via prioritized synchronization and trajectory models. SIAM J. Control Optim. 33-2: 469-497.
Thistle, J. G., Malhamé, R. P., Hoang, H. H., and Lafortune, S. 1995. Blocking, modularity, and feature interactions in distributed systems. Preprint.
Wonham, W. M., and Ramadge, P. J. 1987. On the supremal controllable sublanguage of a given language. SIAM J. Control Optim. 25-3: 637-659.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Barrett, G., Lafortune, S. Bisimulation, the Supervisory Control Problem and Strong Model Matching for Finite State Machines. Discrete Event Dynamic Systems 8, 377–429 (1998). https://doi.org/10.1023/A:1008301317459
Issue Date:
DOI: https://doi.org/10.1023/A:1008301317459