Decentralized Control of Petri Nets

Supervision based on place invariants (SBPI) is an efficient technique for the supervisory control of Petri nets. In this paper we propose extensions of the SBPI to a decentralized control setting. In our setting, a decentralized supervisor consists of local supervisors, each controlling and observing a part of the Petri net. We consider both versions of decentralized control, with communication, and with no communication. In the case of communication, a local supervisor may receive observations of events that are not locally observable and send enabling decisions concerning events that are not locally controllable. In the first part of the paper we propose efficient algorithms for the design of decentralized supervisors, based on the extension of the SBPI concept of admissibility that we define. Then, in the second part of the paper, we propose the design of decentralized supervisors based on transformations to admissible constraints. The feasibility of this problem is demonstrated with a simple integer programming approach. This approach can incorporate communication between local supervisors as well as communication constraints.