  One of the main drawbacks while implementing the interaction between a plant
and a supervisor, synthesised by the supervisory control theory of
\citeauthor{RW:1987}, is the inexact synchronisation. \citeauthor{balemiphdt}
was the first to consider this problem, and the solutions given in his PhD
thesis were in the domain of automata theory. Our goal is to address the issue
of inexact synchronisation in a process algebra setting, because we get
concepts like modularity and abstraction for free, which are useful to further
analyze the synthesised system. In this paper, we propose four methods to check
a closed loop system in an asynchronous setting such that it is branching
bisimilar to the modified (asynchronous) closed loop system. We modify a given
closed loop system by introducing buffers either in the plant models, the
supervisor models, or the output channels of both supervisor and plant models,
or in the input channels of both supervisor and plant models. A notion of
desynchronisable closed loop system is introduced, which is a class of
synchronous closed loop systems such that they are branching bisimilar to their
corresponding asynchronous versions. Finally we study different case studies in
an asynchronous setting and then try to summarise the observations (or
conditions) which will be helpful in order to formulate a theory of
desynchronisable closed loop systems.
