A UNIFIED APPROACH TO CONTROL-PROBLEMS IN DISCRETE-EVENT PROCESSES

Control theory of discrete event processes has been developped in recent years by Ramadge and Wonham. Their framework is based on formal language theory and control theoretic ideas such as controllability and observability. In this paper, we focus on the automata modeling the processes and the specifications, rather than on the sets of possible or acceptable sequences. By adopting this slightly different point of view, we show that the main results of control theory can be obtained in a simple, uniform way. Centralized control problem, observation problems and distributed control problems are stated as particular cases of what we call design problems. With the help of two basic constructions on automata, we show that necessary and sufficient conditions for the existence of solutions are all particular cases of a general lemma on the solutions of design problems. All the results are effective, in the sense that they yield immediate algorithms for the design of controllers.