Starts with a brief review of the history and the application areas considered in the literature. The author then proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis. In particular, one section is devoted to marked graphs, the concurrent system model most amenable to analysis. Introductory discussions on stochastic nets with their application to performance modeling, and on high-level nets with their application to logic programming, are provided. Also included are recent results on reachability criteria. Suggestions are provided for further reading on many subject areas of Petri nets. >

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Petri nets: Properties, analysis and applications

This paper surveys recent research on the application of Petri net models to the analysis and synthesis of controllers for discrete event systems. Petri nets have been used extensively in applications such as automated manufacturing, and there exists a large body of tools for qualitative and quantitative analysis of Petri nets. The goal of Petri net research in discrete event systems is to exploit the structural properties of Petri net models in computationally efficient algorithms for computing controls. We present an overview of the various models and problems formulated in the literature focusing on two particular models, the controlled Petri nets and the labeled nets. We describe two basic approaches for controller synthesis, based on state feedback and event feedback. We also discuss two efficient techniques for the on-line computation of the control law, namely the linear integer programming approach which takes advantage of the linear structure of the Petri net state transition equation, and path-based algorithms which take advantage of the graphical structure of Petri net models. Extensions to timed models are briefly described. The paper concludes with a discussion of directions for future research.

http://www.mne.psu.edu/ray/me597DESandSymbolicDyn/hollowayKroghGiua97.pdf

A Survey of Petri Net Methods for Controlled Discrete EventSystems

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Abstract interpretation

The structure theory of Place/Transition net systems is surveyed - incorporating new contributions - in a tutorial style, mainly from a linear algebraic perspective Topics included are: state equation based analysis of safety properties (e.g., boundedness, mutual exclusion, deadlock-freeness, etc.), linear invariants, siphons and traps, implicit places and their application to improve the accuracy of the state equation, and rank theorems (structural conditions for liveness and boundedness based on the rank of the incidence matrix).

Linear algebraic and linear programming techniques for the analysis of Place/Transition net systems

s of type t o k e n . It also has a precondition saying that the value of the token in c o 1 must be y e 11 ow. If the precondition is satisfied, the processor may fire, consuming the token in the store. Upon firing, it produces two tokens, one in c o l with value r e d , and one in s with value t okenval. Informally, the processor may fire only when the traffic light is yellow. As a result of firing the processor, the traffic light turns red, a t the same time signaling the other light that it may turn green. T h e specification of the other processors is very similar and so is omitted. T h e specification of y2 r does not contain a conditional statement. This means that its behavior does not depend on the values of the consumed tokens. Consequently, it is very similar to the transitions in P/T nets. For this reason, a processor whose behavior is not conditional is often called a transition. This class of processors is important because we can apply analysis techniques like Sand T-invariants to ExSpect specifications only if the specification consists entirely of transitions. ExSpect has a tool to transform any specification into such a transitions-only specification with the same dynamic behavior.

Understanding Petri Nets

Petri nets are a versatile modeling device for studying the structure and control of concurrent systems. Petri nets and related graph models have been used for modeling a wide variety of systems from computers to social systems. In order to introduce this interesting modeling device to the researcher in control theory, this paper discusses Petri nets in the context of the state equation for a linear discrete-time system. The controllability concept of dynamic systems is applied to Petri nets for the first time. It is also shown that the controllability and reachability of a Petri net are related to maximal matchings of its bipartite graph.

T. Murata

Papers

State equation, controllability, and maximal matchings of petri nets