  Conventional supervisory control theory assumes full synchronization between
the supervisor and the plant. This assumption is violated in a networked-based
communication setting due to the presence of delays, and this may result in
incorrect behavior of a supervisor obtained from conventional supervisory
control theory. This paper presents a technique to synthesize a networked
supervisor handling communication delays. For this purpose, first, a networked
supervisory control framework is provided, where the supervisor interacts with
the plant through control and observation channels, both of which introduce
delays. The control channel is FIFO, but the observation channel is assumed to
be non-FIFO so that the observation of events may not necessarily be received
by the supervisor in the same order as they occurred in the plant. It is
assumed that a global clock exists in the networked control system, and so the
communication delays are represented in terms of time. Based on the proposed
framework, a networked plant automaton is achieved, which models the behavior
of the plant under the effects of communication delays and disordered
observations. Based on the networked plant, the networked supervisor is
synthesized, which is guaranteed to be (timed networked) controllable,
nonblocking, time-lock free, (timed networked) maximally permissive, and
satisfies control requirements for the plant.
