Controlled Petri Nets: A Tutorial Survey

This paper surveys recent research on the synthesis of controllers for discrete event systems (DESs) modeled by controlled Petri nets (CtlPNs). Petri nets have been used extensively in applications such as automated manufacturing [6], and there exists a large body of tools for qualitative and quantitative analysis of Petri nets [28]. For control, Petri nets offer a structured model of DES dynamics that can be exploited in developing efficient algorithms for controller synthesis. The following section presents the basic untimed CtlPN model, discusses special classes of CtlPNs, and gives an overview of the various control problems that have been formulated and solved in the literature. Section 3 describes state feedback controllers for CtlPNs and the general conditions that must be satisfied for a state feedback control policy to exist to prevent the CtlPN from reaching a given set of forbidden markings. In Sect. 4, control of the sequential behavior of a CtlPN is considered. We summarize methods for converting event-based sequential control problems into state feedback problems. We then present two general approaches to computing state feedback policies, namely, the linear integer programming approach of Li and Wonham (Sect. 5) and the path-based approach introduced by Holloway and Krogh (Sect. 6). The paper concludes with a discussion of several directions for further research in Sect. 7. 2 Controlled Petri Net