Control (management)

Engineering

Pure mathematics

Petri net

Control engineering

Automatic control

Theoretical computer science

Field (mathematics)

Systems engineering

Computer science

Limit (mathematics)

Management science

Physics

Mathematics

Optics

Focus (optics)

Mathematical analysis

Artificial intelligence

Geometry

Rotation formalisms in three dimensions

Software engineering

Programming language

Process architecture

Deadlock

Perspective (graphical)

State (computer science)

Annual Reviews in Control

The goal of this paper is to overview the historical development of the field of Petri nets (PNs) from a Systems Theory and Automatic Control perspective. It is intentionally not meant to be comprehensive: we limit ourselves to outline, through selected representative topics, some of the conceptual issues studied in the literature. In a first part we retrace the emergence of some basic net concepts to provide a broad view of the family of PN formalisms. Then we focus, more specifically, on the use of Petri nets within Automatic Control. Discrete net models have been considered since the middle of the 70s and starting since the late 80s have also been used for addressing classical problems, such as supervisory and deadlock control, state estimation, diagnosis, and so on. The double benefit is the ability to model a larger class of systems and to provide efficient algorithms for solving certain of those problems. We also discuss new approaches based on continuous and hybrid nets, which have been developed within the Automatic Control community.

Petri nets and Automatic Control: A historical perspective