Designing observation functions in supervisory control

This paper discusses the problem of designing an observation function as coarsest as possible in supervisory control of discrete event dynamic systems. Some algebraic properties of two sets consisting of observation functions for which the given desirable behavior is realizable are investigated:these sets with a partial ordering turn out not to possess largest elements. Two natural methods of obtaining an observation function, which is frequently coarser than the identity mapping, are also presented. An example illustrates the use of these methods.