Intersection-Based Decentralized Supervisory Control of Probabilistic Discrete Event Systems

In our previous article, we have considered the supervisory control of the probabilistic discrete event systems (PDESs) under the centralized framework. In this article, we continue to investigate the decentralized probabilistic supervisory control issue of PDESs. The intersection-based control architecture is adopted, and the notion of the probabilistic intersection-based coobservability and its verification algorithm are presented. It is shown that this observability and the probabilistic controllability act as the necessary and sufficient conditions for the existence of the intersection-based decentralized probabilistic supervisors. Moreover, a working example is provided to illustrate the proposed concepts, the obtained results, and the potential application of the proposed control approaches.