Partial Observation in Distributed Supervisory Control of Discrete-Event Systems

Distributed supervisory control is a method to synthesize local controllers in discrete-event systems with a systematic observation of the plant. Some works were reported on extending this method by which local controllers are constructed so that observation properties are preserved from monolithic to distributed supervisory control, in an up-down approach. In this paper, we find circumstances in which observation properties are preserved from monolithic to distributed supervisory control. Local observation properties, i.e. local normality and local relative observability are employed for investigating observation properties of each local controller, which are constructed by any localization algorithm that preserves control equivalency to the monolithic supervisor with respect to the plant. These properties enable us to investigate the observation properties from monolithic to distributed supervisory control. Moreover, observation equivalence property is defined according to the control equivalence in a distributed supervisory control with partial observation. It is proved that with preserving observation equivalence of the local controllers to the monolithic supervisor, the control equivalence is satisfied, if and only if the intersection of local event sets is a subset of or equal to the global observable event set.