Decentralized Supervisory Control of Discrete Event Systems: An Arborescent Architecture to Realize Inference-Based Control

The two simplest language-based decentralized controls of discrete event systems are called conjunctive and permissive (C&P) and disjunctive and antipermissive (D&A) controls. On the other side, inference-based control is the most general language-based decentralized control. In this paper, we propose a decentralized control method, called arborescent control, which constructs and uses a tree-like control architecture that depends on the control objective. Each node π of the tree is a disjunction or conjunction of the enabling/disabling decisions of the two children of π. We show that if inference-based control is applicable to the control objective, then every leaf of the obtained tree is a C&P or D&A control. This means that by combining adequately C&P and D&A controls, we can realize every control objective that is realizable by inference-based control.