Static and Dynamic Partitions of Inequalities: A Unified Methodology for Supervisor Simplification

In the context of automated manufacturing systems, supervisor simplification is drawing increasing attention. As a special class of state specifications, generalized mutual exclusion constraints (GMECs) are a typical kind of supervisory control of Petri nets. In this note, we first propose static and dynamic partitions to reduce the size of supervisor by partitioning inequalities, i.e., GMECs, into redundant and necessary ones. The former considers the specifications themselves and exhibits higher efficiency; while the latter takes into account both specifications and reachable markings and achieves more economical supervisors. In an incremental manner, we develop Type I supervisor simplification method which has a compromised efficiency and complexity. In an integrated manner, we propose Type II supervisor simplification method that further improves efficiency and eases computational complexity. All techniques proposed in this note can be realized in an algebraic manner. Examples are presented for the sake of illustration as well as demonstration.