Structuring multilevel discrete-event systems with dependence structure matrices

Despite the correct-by-construction property, one of the major drawbacks of supervisory control synthesis is state-space explosion. Several approaches have been proposed to overcome this computational difficulty, such as modular, hierarchical, decentralized, and multilevel supervisory control synthesis. Unfortunately, the modeler needs to provide additional information about the system's structure or controller's structure as input for most of these nonmonolithic synthesis procedures. Multilevel synthesis assumes that the system is provided in a tree-structured format, which may resemble a system decomposition. In this paper, we present a systematic approach to transform a set of plant models and a set of requirement models provided as extended finite automata into a tree-structured multilevel discrete-event system to which multilevel supervisory control synthesis can be applied. By analyzing the dependencies between the plants and the requirements using dependence structure matrix techniques, a multilevel clustering can be calculated. With the modeling framework of extended finite automata, plant models and requirements depend on each other when they share events or variables. We report on experimental results of applying the algorithm's implementation on several models available in the literature to assess the applicability of the proposed method. The benefit of multilevel synthesis based on the calculated clustering is significant for most large-scale systems.