Desynchronisability of (partial) closed loop systems

The task of implementing supervisory controllers is non-trivial, even though there are different theories that allow automatic synthesis of such controllers in the form of automata. One of the reasons for this discord, is the asynchronous interaction between a plant and its controller in implementations, whereas the existing supervisory control theories assume synchronous interaction. As a consequence the implementation suffers from the so-called inexact synchronization problem. To address this issue, we find sufficient conditions under which a synchronous closed loop system is branching bisimilar to its corresponding asynchronous closed loop system. Furthermore, we extend this result to include interaction of plant or supervisor with its environment.