Coinduction in Control of Partially Observed Discrete-Event Systems

Coalgebra and coinduction provide new results and insights for the supervisory control of discrete-event systems (DES) with partial observations. In the case of full observations, coinduction has been used to define a new operation on languages called supervised product, which represents the tuple of languages of the supervised system. The first language acts as a supervisor and the second as an open-loop system (plant). We show first that the supervised product is equal to the infimal controllable superlanguage of the supervisor’s (specification) language with respect to the plant language. This can be generalized to the partial observation case, where the supervised product is shown to be equal to the infimal controllable and observable superlanguage. A modification on the supervised product is presented, which corresponds to the control policy for with the issue of observability is separated from the issue of controllability. The operation defined by coinduction is shown to be equal to the infimal observable superlanguage.