Abstract
An abstract hierarchical control theory is developed for discrete-event systems, based on the concepts of control structures and observers. Control structure is an abstract generalization of the family of controllable sublanguages in the Ramadge-Wonham framework. We establish a general version of Zhong's hierarchical consistency by first achieving control consistency — preservation of control structures through the aggregation mapping in a two-level hierarchy. For a refinement of hierarchical consistency with preservation of nonblocking, the concept of observer is introduced via congruences on nondeterministic transition structures.
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J. C. M. Baeten and W. P. Weijland.Process Algebra. Cambridge University Press, 1990. Cambridge Tracts in Theoretical Computer Science 18.
B. A. Brandin.Real-Time Supervisory Control of Automated Manufacturing Systems. Ph.D. thesis, Department of Electrical Engineering, University of Toronto, 1993, Also appears as Technical Report 9302, Systems Control Group, Department of Electrical Engineering, University of Toronto, February, 1993.
B. A. Brandin and W. M. Wonham. Supervisory control of timed discrete-event systems.IEEE Transactions on Automatic Control, 39(2):329–342, 1994.
Y. Brave and M. Heymann. Control of discrete event systems modeled as hierarchical state machines.IEEE Transactions on Automatic Control, 38(12):1803–1819, December 1993.
P. E. Caines and Y.-J. Wei. The hierarchical lattices of a finite machine.Systems and Control Letters, pages 257–263, July 1995.
R. Cieslak, C. Desclaux, A. S. Fawaz, and P. Varaiya. Supervisory control of discrete-event processes with partial observations.IEEE Transactions on Automatic Control, 33(3):249–260, March 1988.
K. Inan. An algebraic approach to supervisory control.Mathematics of Control, Signals, and Systems, 5:151–164, 1992.
M. Johnson and C. N. G. Damphey. On the value of commutative diagrams in information modelling. In M. Nivat, C. Rattray, T. Rus, and G. Scollo, editors,Algebraic Methodology and Software Technology, Enschede 1993, pages 45–58. Springer-Verlag, 1993. Workshops in Computing, Series edited by by Professor C. J. van Rijsbergen.
Y. Li.Control of Vector Discrete-Event Systems. Ph.D. thesis, Department of Electrical Engineering, University of Toronto, 1991, Also appears as Technical Report 9106, Systems Control Group, Department of Electrical Engineering, University of Toronto, July, 1991.
Y. Li and W. M. Wonham. Control of vector discrete-event systems 1 — the base model.IEEE Transactions on Automatic Control, 38(8):1214–1227, August 1993.
F. Lin and W. M. Wonham. Decentralized supervisory control of discrete-event systems.Information Sciences, 44:199–224, 1988.
F. Lin and W. M. Wonham. On observability of discrete-event systems.Information Sciences, 44:173–198, 1988.
M. D. Mesarović, D. Macko, and Y. Takahara.Theory of Hierarchical, Multilevel Systems. Academic, New York, 1970.
R. Milner.A Calculus of Communicating Systems, volume 92 ofLNCS. Springer-Verlag, New York, 1980.
R. Milner.Communication and Concurrency. Prentice Hall International Series in Computer Science. Prentice Hall, New York, 1989.
P. J. Ramadge.Control and Supervision of Discrete Event Processes. Ph.D. thesis, Department of Electrical Engineering, University of Toronto, 1983.
P. J. Ramadge and W. M. Wonham. Supervision of discrete event processes. InProc. of 21st Conf. on Decision and Control, pages 1228–1229, 1982.
P. J. Ramadge and W. M. Wonham. Modular feedback logic for discrete event systems.SIAM J. Control and Optimization, 25(5):1202–1218, 1987.
P. J. Ramadge and W. M. Wonham. The control of discrete event systems.Proc. IEEE, Special Issue on Discrete Event Dynamic Systems, 77(1):81–98, January 1989.
K. Rudie and W. M. Wonham. Think globally, act locally: decentralized supervisory control.IEEE Transactions on Automatic Control, 37(11):1692–1708, 1992.
Y. Willner and M. Heymann. On supervisory control of concurrent discrete-event systems. Technical Report 9009, Computer Science Department, Israel Institute of Technology, Technion, 1990.
K. C. Wong.An Algebraic Description of Hierarchical Control in Discrete-Event Systems. M.A.Sc thesis, Department of Electrical Engineering, University of Toronto, 1990.
K. C. Wong.Discrete-Event Control Architecture: An Algebraic Approach. Ph.D. thesis, Department of Electrical Engineering, University of Toronto, 1994, Also appears as Technical Report 9407, Systems Control Group, Department of Electrical Engineering, University of Toronto, July, 1994.
K. C. Wong and W. M. Wonham. Hierarchical control of timed discrete-event systems.Discrete Event Dynamic Systems: Theory and Applications, 6:275–306, 1996.
K. C. Wong and W. M. Wonham. Hierarchical and modular control of discrete-event systems. InProc. of Thirtieth Annual Allerton Conference on Communication, Control, and Computing, pages 614–623, Monticello, Illinois, September–October 1992.
W. M. Wonham. Towards an abstract internal model principle.IEEE Transactions on Systems, Man, and Cybernetics, SMC-6(11):735–740, November 1976.
W. M. Wonham. Some current research directions in control of discrete-event systems.Preprint: European Control Conference, July 1991.
W. M. Wonham and P. J. Ramadge. Modular supervisory control of discrete event systems.Mathematics of Control, Signal and Systems, 1(1):13–30, 1988.
H. Zhong.Hierarchical control of discrete-event systems. Ph.D. thesis, Department of Electrical Engineering, University of Toronto, 1992, Also appears as Technical Report 9208, Systems Control Group, Department of Electrical Engineering, University of Toronto, July, 1992.
H. Zhong and W. M. Wonham. On the consistency of hierarchical supervision in discrete-event systems.IEEE Transactions on Automatic Control, 35(10):1125–1134, October 1990.
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Wong, K.C., Wonham, W.M. Hierarchical control of discrete-event systems. Discrete Event Dyn Syst 6, 241–273 (1996). https://doi.org/10.1007/BF01797154
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DOI: https://doi.org/10.1007/BF01797154