Synthesis of Maximally-Permissive Supervisors for the Range Control Problem

Abstract

We investigate the supervisor synthesis problem for centralized partially-observed discrete event systems subject to safety specifications. It is well known that this problem does not have a unique supremal solution in general. Instead, there may be several incomparable locally maximal solutions. One then needs a mechanism to select one locally maximal solution. Our approach in this paper is to consider a lower bound specification on the controlled behavior, in addition to the upper bound for the safety specification. This leads to a generalized supervisory control problem called the range control problem. While the upper bound captures the (prefix-closed) legal behavior, the lower bound captures the (prefix-closed) minimum required behavior. We provide a synthesis algorithm that solves this problem by effectively constructing amaximally-permissive safe supervisor that contains the required lower bound behavior. This is the first algorithm with such properties, as previous works solve either the maximally-permissive safety problem (with no lower bound), or the lower bound containment problem (without maximal permissiveness).

DOI: 10.1109/TAC.2016.2644867

Cite this paper

@article{Yin2017SynthesisOM, title={Synthesis of Maximally-Permissive Supervisors for the Range Control Problem}, author={Xiang Yin and St{\'e}phane Lafortune}, journal={IEEE Trans. Automat. Contr.}, year={2017}, volume={62}, pages={3914-3929} }