Supervision Based on Place Invariants: A Survey

The supervision based on place invariants (SBPI) is an efficient technique for the supervisory control of Petri nets. This paper reveals the significance of the SBPI based on a literature survey, applications, and an analysis of problems and supervisory settings that can be addressed using SBPI. Special attention is given to the various settings within which the problem can be formulated. Such settings can be distinguished based on the concurrency type, the type of controllability and observability, and the centralized or decentralized type of supervision. As we show, it is possible to approach the most general settings in a purely structural way, without resorting to reachability analysis. We begin by describing the SBPI problem and the literature methods that address this problem or are related to it. Then, we proceed to show classes of problems that can be reduced to the SBPI problem. In the SBPI, the specification is described as a system of inequalities that the Petri net marking must satisfy at any time. However, as we show, problems involving more general specifications can be approached in the SBPI setting, sometimes under additional assumptions, by performing net and/or specification transformations. Four of the specifications we will consider are logic constraints, language specifications, disjunctions of linear constraints, and liveness. We conclude with a presentation of possible applications of the SBPI approach to programming with semaphores, fault tolerance, and synchronic-distance based designs.