Supervisory control of discrete-event systems in an asynchronous setting

In conventional supervisory control theory, a plant and supervisor are supposed to work synchronously such that enabling an event by the supervisor, execution of it in the plant, and observation of the executed event by the supervisor all occur at once. Therefore, these occurrences are all captured by means of a single event. However, when a supervisor synthesized from conventional supervisory control theory is implemented in real life, it will face problems since exact synchronization can hardly happen in practice due to delayed communications. In this paper, we propose a synthesis technique to achieve a supervisor that does not face the problems caused by inexact synchronization. For this purpose, we first introduce an asynchronous setting in which enablement, execution, and observation of an event do not occur simultaneously but with some delay. We present a model representing the behavior of the plant in the asynchronous setting which we call the asynchronous plant. For the asynchronous plant, we present an algorithm synthesizing an asynchronous supervisor which satisfies (asynchronous) controllability and nonblockingness.