Modular control of large distributed discrete event systems

Coalgebra and coinduction provide new results and insights for modular supervisory control of discrete-event systems (DES), where the overall system is composed of subsystems that are combined in synchronous (parallel) product. Modular supervisory control is studied within the coalgebraic framework. Coinduction has been used to define an operation on languages called supervised product, and synchronous product is defined by coinduction. We have shown recently that the supremal controllable sublanguage of a given language can be defined by coinduction as well. We study the commutativity between the synchronous product and supremal controllable and normal sublanguage. The results guarantee that under the conditions derived in the paper control synthesis can be done locally without affecting the optimality of the solution.