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On the control of discrete-event systems

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Three Decades of Mathematical System Theory

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 135))

Abstract

In this paper we have provided an overview of one trend among others in the development of a control theory for discrete-event systems. In view of the relatively long history of prior approaches to discrete-event control design (notably discrete-event system simulation, and analysis via Petri nets, starting in the 1960s; and investigations via queueing theory and its variants, including perturbation analysis, from the early 1970s) it is perhaps surprising that attempts to evolve a synthetic, control-theoretic overview of the problem area, especially in its qualitative, logical aspects, have been both few in number and recent in appearance. In any case, it can fairly be said that control of DES is now an established branch of control theory.

The current studies of control of DES in its qualitative aspects highlight the thesis that control science is defined in terms of problems and concepts, not in terms of techniques. In general control science may be described as the study of how information and dynamics are brought into purposeful interaction. Stimulated by the demands of technology and by developments in computer science, control science has entered a new phase, where discreteness, modularity and communication are fundamental. Alongside the traditional mathematics of control theory like differential equations and operator theory, new techniques are entering the field from automaton theory, formal language and formal logic; while developments in computer programming methodology, as for instance abstract data structures and the object-oriented paradigm, may strongly influence the way this new mathematics (new in control theory) will be put to work. For both researchers and educators in the control field, the challenges are plentiful.

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Authors and Affiliations

  1. Systems Control Group, Dept. of Electrical Engineering, University of Toronto, M5S 1A4, Toronto, Ontario, Canada

    W. M. Wonham

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  1. W. M. Wonham
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Hendrik Nijmeijer Johannes M. Schumacher

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© 1989 Springer-Verlag

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Wonham, W.M. (1989). On the control of discrete-event systems. In: Nijmeijer, H., Schumacher, J.M. (eds) Three Decades of Mathematical System Theory. Lecture Notes in Control and Information Sciences, vol 135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0008476

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  • DOI: https://doi.org/10.1007/BFb0008476

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51605-7

  • Online ISBN: 978-3-540-46709-0

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