Desynchronisability of (partial) closed loop systems

The task of implementing a supervisory controller is non-trivial, even though there are different theories that allow automatic synthesis of these controllers in the form of automata. One of the reasons for this discord is due to 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 synchronisation problem. In this paper we address the issue of inexact synchronisation in a process algebraic setting, by solving a more general problem of refinement. We construct an asynchronous closed loop system by introducing a communication medium in a given synchronous closed loop system. Our goal is to find sufficient conditions under which a synchronous closed loop system is branching bisimilar to its corresponding asynchronous closed loop system. Furthermore, we extend our results to a class of synchronous closed loop systems called partial synchronous closed loop systems, whose alphabet contains external actions of both the plant and its controller that do not result in interaction.