Distributed Supervisory Control with Partial Observation

Distributed supervisory control is a method to synthesize local controllers without any restriction on observation of the plant. Since the set algebra preserves relationships between variables and provides a simpler way to develop theories, the observation properties are redefined and corresponding propositions are proved by set algebra, in this paper. Moreover, we define new observation properties, i.e. local normality and local relative observability for the local controllers which constructed by any localization algorithm that preserves control equivalent to monolithic supervisor w.r.t. the plant. These properties enable us to investigate the observation problem from monolithic to distributed supervisory control. Furthermore, observation equivalence property is defined corresponding to the control equivalence in distributed supervisory control with partial observation. It is proved that, providing observation equivalence of the local controllers to the monolithic supervisor w.r.t. the plant, the control equivalence is satisfied, if and only if the intersection of local events sets is a subset or equal to the global observable events set.