Abstract
The concept of observer was introduced in previous work by the authors on a hierarchical control theory of discrete-event systems (DES). It was shown that the observer property of the “causal reporter” map, which in this theory models information flow in a hierarchical DES, plays a role in ensuring that a nonblocking supervisor at a given level of a hierarchy does not cause blocking in the level below. In this paper, we investigate the following problem: Given a causal reporter map that is not an observer, how can we design an observer by modifying this map? In case the latter is represented by a finite Mealy automaton, an effective computational algorithm is developed for computing an observer with the coarsest possible equivalence kernel that is finer than that of the given map. Three examples are provided for illustration.
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References
Arnold, A. 1994. Finite Transition Systems. Prentice Hall.
Burris, S., and Sankappanavar, H. P. 1981. A Course in Universal Algebra. New York: Springer-Verlag.
Fernandez, J.-C. 1990. An implementation of an efficient algorithm for bisimulation equivalence. Science of Computer Programming 13: 219-236.
Guan, Y. 1997. Implementation of Hierarchical Observer Theory. M.A.Sc. thesis, Department of Electrical and Computer Engineering, University of Toronto.
Hubbard, P., and Caines, P. E. 2002. Dynamical consistency in hierarchical supervisory control. IEEE Transactions on Automatic Control 47(1): 37-52, January.
Lin, F., and Wonham, W. M. 1988. Decentralized supervisory control of discrete-event systems. Information Sciences 44: 199-224.
Milner, R. 1989. Communication and Concurrency. New York: Prentice Hall.
Pu, K. Q. 2000. Modeling and Control of Discrete-Event Systems with Hierarchical Abstractions. M.A.Sc. thesis, Department of Electrical and Computer Engineering, University of Toronto.
Ramadge, P. J., and Wonham, W. M. 1987. Supervisory control of a class of discrete-event processes. SIAM J. Control and Optimization 25(1): 206-230.
Sifakis, J. 1982. A unified approach for studying the properties of transition systems. Theoretical Computer Science 18: 227-258.
Wonham, W. M. 2002. Notes on Control of Discrete-Event Systems: ECE 1636F/1637S. Department of Electrical and Computer Engineering, University of Toronto. Can be downloaded from www.control.utoronto.ca/people/profs/wonham/wonham.html.
Wonham, W. M. 1976. Towards an abstract internal model principle. IEEE Transactions on Systems, Man, and Cybernetics SMC-6(11): 735-740, November.
Wong, K. C. 1998. On the complexity of projections of discrete-event systems. IEEE Workshop on Discrete Event Systems. Italy: Cagliari (Sardinia), 201-206, August.
Wong, K. C., Thistle, J. G., Malhamé, R. P., and Hoang, H.-H. 2000. Supervisory control of distributed systems: conflict resolution. Discrete Event Dynamical Systems: Theory and Applications 10(1): 131-186.
Wong, K. C., and Wonham, W. M. 1996. Hierarchical control of discrete-event systems. Discrete Event Dynamic Systems: Theory and Applications 6(3): 241-273, July.
Wong, K. C., and Wonham, W. M. 1998. Modular control and coordination of discrete-event systems. Discrete Event Dynamic Systems: Theory and Applications 8(3): 247-297.
Wong, K. C., and Wong, W. M. 2000. On the computation of observers in discrete-event systems. In 2000 Conference on Information Sciences and Systems. Princeton, NJ, TP1-7 to TP1-12, March.
Zhong, H., and Wonham, W. M. 1990. On the consistency of hierarchical supervision in discrete-event systems. IEEE Transactions on Automatic Control 35(10): 1125-1134.
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Wong, K., Wonham, W. On the Computation of Observers in Discrete-Event Systems. Discrete Event Dynamic Systems 14, 55–107 (2004). https://doi.org/10.1023/B:DISC.0000005010.55515.27
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DOI: https://doi.org/10.1023/B:DISC.0000005010.55515.27