Abstract
This paper introduces a formal framework to logically analyze and control real-time discrete event systems (RTDESs). Time Petri nets are extended to controlled time Petri nets (CtlTPNs) to model the dynamics of RTDESs that can be controlled by real-time supervisors. The logical behaviors of CtlTPNs are represented by control class graphs (CCGs) which are untimed automata with timing and control information in their state transition labels. We prove that the CCG corresponding to a CtlTPN expresses completely the logical behavior of the CtlTPN. The real-time supervisor is based on a nondeterministic logical supervisor for the CCG, including the delay for control computations to ensure the supervisor is acceptable in a true real-time environment. We prove the existence of a unique maximal controllable sublanguage of a given specification language and present an algorithm to construct the sublanguage. We also prove that the real-time supervisor meets the prespecified real-time behavior and present an online control algorithm to implement real-time supervisors. The concepts and algorithms are illustrated for an example of packet reception processes in a communication network.
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Alur, R., Courcoubetis, C., and Dill, D. L. 1993. Model checking in dense real time. Information and Computation, 104(1):2–34.
Alur, R. and Dill, D.L. 1994. A theory of timed automata. Theoretical Computer Science, 126:183–235.
Berthomieu, B. and Diaz, M. 1991. Modeling and verification of time dependent systems using time Petri nets. IEEE Transactions on Software Engineering, 17(3).
Brandin, B. and Wonham, M. 1994. Supervisory control of timed discrete event systems. IEEE Transactions on Automatic Control, 39(2):329–342.
Brave, Y. and Heymann, M. 1988. Formulation and control of a class of real–time discrete–event processes. Proceedings of the 27th IEEE Conf. on Decision and Control, pp. 1131–1132.
Glynn, P. A GSMP formalism for discrete–event systems. Proceedings of the IEEE, 77(2):14–23.
Golaszewski, C. and Ramadge, P. 1988. Discrete event processes with arbitrary controls. in M.J. Denham and A.j. Laub, editors, Advanced Computing Concepts and Techniques in Control Engineering, Springer–Verlag NATO ASI Series, New York, pp. 459–469.
Ho, Y. 1989. Dynamics of discrete–event systems. Proceedings of the IEEE, 77(1):3–6.
Lafortune, S. and Chen, E. 1990. The infimal closed controllable superlanguage and its application in supervisory control. IEEE Trans. on Automatic Control, 35(4):398–405.
Merlin, P. 1974. A Study of the recoverability of Computer System. PhD thesis, Univ. of California, Irvine.
Murata, T. 1989. Petri nets: properties, analysis and applications. Proceedings of the IEEE, 77(4):541–580.
Ostroff, J. and Wonham, M. 1990. A framework for real–time discrete event control. IEEE Transactions on Automatic Control, 35(4):386–397.
O'Young, S. 1991. On the synthesis of supervisors for timed discrete event processes. Systems Control Group, University of Toronto, Toronto, Canada, Technical Report No. 9107.
Ramadge, P. and Wonham, M. 1989. The control of discrete–event systems. Proceedings of the IEEE, 77(1):81–97.
Sathaye, A. and Krogh, B. 1992. Logical analysis and control of timed Petri nets. Proceedings of the 31st IEEE Conference on Decision and Control, Tuscon, Arizona.
Sathaye, A. 1993. Logical Analysis and Control of Real–Time Discrete Event Systems. PhD Thesis, Carnegie Mellon University, Department of Electrical and Computer Engineering, Pittsburgh, Pennsylvania.
Sathaye, A. and Krogh, B. H. 1993. Synthesis of Real–Time Supervisors for controlled time Petri nets. Proceedings of the 32nd IEEE Conference on Decision and Control, San Antonio, Texas.
Sathaye, A. and Krogh, B. H. 1994. Application of Supervisor Synthesis for controlled time Petri nets to Real–Time Database Systems. Proceedings of the 1994 American Control Conference, Baltimore, Maryland.
Sreenivas, R. S. and Krogh, B. H. 1991. On Condition/Event systems with discrete state realization. Discrete Event Dynamic Systems: Theory and Applications, (1):209–236.
Wong–Toi, H. and Hoffmann, G. 1991. The control of dense real–time discrete event systems. Proceedings of the 30th IEEE Conf. on Decision and Control, pp. 1527–1528.
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Sathaye, A.S., Krogh, B.H. Supervisor Synthesis for Real-Time Discrete Event Systems. Discrete Event Dynamic Systems 8, 5–35 (1998). https://doi.org/10.1023/A:1008252325849
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DOI: https://doi.org/10.1023/A:1008252325849