Supervisory Control of Networked Discrete Event Systems to Achieve a Required Language

Because of the wide use of networks, supervisory control of networked discrete event systems becomes more and more important. Since the languages generated by a networked supervisor is nondeterministic due to communication delays and losses, large and small languages are defined. While the large language has been investigated in the literature, the small language has not. In this article, we investigate the small language, which is needed for a supervised system to perform some required tasks. Network S-observability is introduced to capture the necessary and sufficient condition for the existence of a networked supervisor achieving a given small language. A method is developed to check if network S-observability is satisfied. We also show that the infimal controllable and network S-observable superlanguage of a language exists and can be calculated using a method developed in this article. Finally, the theoretical results are illustrated by applying them to an autonomous service robot.