Abstraction-based Synthesis of Timed Supervisors for Time-Weighted Systems

The Ramadge-Wonham supervisory control theory has shown to be useful in dealing with task routing and coordination under various types of logic constraints in complex systems. Recently, a new time optimal supervisory control paradigm has been proposed, which models a plant as a time-weighted discrete-event system and aims for minimizing the makespan of finishing a given finite number of jobs within the system while complying with all pre-specified logic constraints. Considering the high complexity involved in synthesizing a supervisor to ensure a finite makespan (let alone the minimum one), in this paper we propose a deterministic automaton abstraction method which allows model abstraction to be carried out in a distributed fashion, and thus, may potentially reduce the size of a plant significantly so that subsequent time optimal supervisor synthesis can be done in a computationally efficient manner. After showing how to derive a time optimal supervisor based on an abstracted model, we explain how to use such a supervisor for task routing and scheduling.