Natural Projections for the Synthesis of Non-Conflicting Supervisory Controllers

A common strategy in the design of discrete-event systems is to apply synthesis algorithms not to the actual plant model but to an Abstraction that is realised on a significantly smaller state set. Depending on the control objectives, certain conditions are imposed on the plant and on the Abstraction, in order to end up with an appropriate controller. A well known result from the literature is that Abstractions obtained by a so called natural observer can be used for the purpose of non-blocking supervisory control. Despite additional favourable properties of natural observers regarding state count and composed plants, as a condition for non-blocking supervisory control it is restrictive, i.e., sufficient but not necessary. This contrasts the sufficient and necessary condition developed in this paper.