×

Formulas for calculating supremal controllable and normal sublanguages. (English) Zbl 0715.93044

Summary: Supremal controllable and normal sublanguages have been shown to play an important role in supervisor synthesis. We discuss the computation of supremal controllable and normal sublanguages. We derive formulas for both supremal controllable sublanguages and supremal normal sublanguages when the languages involved are closed. As a result, those languages can be computed without applying recursive algorithms. We also discuss those aspects of these formulas.

MSC:

93C55 Discrete-time control/observation systems
68Q45 Formal languages and automata
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Cieslak, R.; Desclaux, C.; Fawaz, A.; Varaiya, P., Supervisory control of discrete-event processes with partial observations, IEEE Trans. Automat. Control, 33, 3, 249-260 (1988) · Zbl 0639.93041
[2] Cho, H.; Marcus, S. I., Supremal and maximal sublanguages arising in supervisor synthesis problems with partial observations, Mathematical Systems Theory, 22, 177-211 (1989) · Zbl 0683.68062
[3] Cho, H.; Marcus, S. I., On supremal languages of class of sublanguages that arise in supervisor synthesis problems with partial observations, Math. Control Signal Systems, 2, 47-69 (1989) · Zbl 0654.93046
[4] Hopcroft, J. E.; Ullman, J. D., Introduction to Automata Theory, Languages and Computation (1979), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0196.01701
[5] Kumar, R.; Garg, V.; Marcus, S. I., Supervisory control of discrete event systems: supremal controllable and observable languages, (Proceedings of the 27th Annual Allerton Conference (1989)), 501-510
[6] Lin, F., On controllability and observability of discrete event systems, (Ph. D. Thesis (1987), Department of Electrical Engineering, University of Toronto)
[7] Lin, F.; Brandt, R. D.; Wonham, W. M., A note on supremal controllable and normal sublanguages, (Proceedings of the 27th Annual Allerton Conference (1989)), 491-500
[8] Lin, F.; Wonham, W. M., Decentralized supervisory control of discrete-event systems, Inform. Sci., 44, 3, 199-224 (1988) · Zbl 0679.68042
[9] Lin, F.; Wonham, W. M., On observability of discrete event systems, Inform. Sci., 44, 3, 173-198 (1988) · Zbl 0644.93008
[10] Lin, F.; Wonham, W. M., Decentralized control and coordination of discrete event systems with partial observations, (Systems Control Group Report No. 8909 (1989), Department of Electrical Engineering, University of Toronto) · Zbl 0821.93002
[11] Lin, F.; Vaz, A. F.; Wonham, W. M., Supervisor specification and synthesis for discrete event systems, Internat. J. Control, 48, 1, 321-332 (1988) · Zbl 0652.93017
[12] Ramadge, P. J.; Wonham, W. M., Supervisory control of a class of discrete event processes, SIAM J. Control Optim., 25, 1, 206-230 (1987) · Zbl 0618.93033
[13] Wonham, W. M.; Ramadge, P. J., Modular supervisory control of discrete event systems, Math. Control Signal Systems, 1, 1, 13-30 (1988) · Zbl 0661.93053
[14] Ramadge, P. J.; Wonham, W. M., The control of discrete event systems, (Proc. IEEE, 77 (1989)), 81-98, 1 · Zbl 0595.93047
[15] Wonham, W. M., A control theory for discrete-event systems, (Denham, M. J.; Laub, A. J., Advanced Computing Concepts and Techniques in Control Engineering. Advanced Computing Concepts and Techniques in Control Engineering, NATO ASI Series, F47 (1988), Springer-Verlag: Springer-Verlag Berlin), 129-169
[16] Wonham, W. M.; Ramadge, P. J., On the supremal controllable sublanguage of a given language, SIAM J. Control Optim., 25, 3, 635-659 (1987)
[17] Zhong, H., Control of discrete-event systems: decentralized and hierarchical control, (M.A.Sc. Thesis (1987), Department of Electrical Engineering, University of Toronto)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.