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Petri net synthesis for discrete event control of manufacturing systems. (English) Zbl 0849.93002
Dordrecht: Kluwer Academic Publishers. xxi, 233 p. (1993).
The final chapter, “Petri nets: past present and future”, presents an overview of the literature on Petri nets, since its inception in 1962. Perhaps it would be more useful as preliminary chapter, so to place the rest of the book in a broader perspective. In fact it is not, and does not pretend to be, an introductory book on Petri nets. It is rather an account of a particular stream of research within the framework of Petri net theory. Unfortunately, as might be expected in view of this orientation, the book is not easily readable.
Petri nets are graphical representations of discrete event systems. For example, they can be used to model manufacturing systems. Nodes of the net are distinguished in places, representing operations and resources, and transitions, representing changes of state. They are connected by the appropriate arcs. Here the attention is focused on the properties of boundedness, liveness, and reversibility that insure satisfactory behavior, including absence of overflow and deadlock and the possibility of error recovering. The feasibility problem is that of finding all the initial conditions of a net that insure such properties. This problem is not yet completely solved, as the authors state in the final chapter.
Petri nets represent the structure of the system. “Basic Petri nets include no notion of time.” However, most significant problems, and feasibility is a case in point, are dynamic problems. Thus, where is the representation of evolution in time? In the book it is confined to the initial definitions and, implicitly, to the description of the Petri net execution algorithm at the end of the book. In this way it does not emerge as clearly as it deserves.
In block diagrams of classical control theory, one may investigate invariance of block properties in an interconnected system, i.e. the possibility that an interconnected system inherit the properties of its component systems. Similarly, the bulk of the book is centered on the derivation of results that insure inheritance of good properties from the subnets of a net to the net itself. This paves the way to various methods of synthesis of Petri nets. A warning on terminology: synthesis here consists in the determination of the structure of the net rather than in some form of control. This use of the word “modeling” is rather confusing.
At times the problem of complexity is mentioned in the book, but it is never really dealt with. Petri nets are an alternative tool for dealing with DES. Today none of the approaches proposed can claim to be completely successful. In this light more space should be devoted to comparative analysis and unification. This is just one of the fields for future research the authors propose right at the end of the book.
All in all, the book can be useful mostly to specialists of the topics covered, who need to be adjourned on this particular stream of research.

MSC:
93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
68-02 Research exposition (monographs, survey articles) pertaining to computer science
90B30 Production models
68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
93A10 General systems
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
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