Nonblocking and Safe Control of Discrete-Event Systems Modeled as Extended Finite Automata

Extended Finite Automata (EFA), i.e., finite automata extended with variables, are a suitable modeling framework for discrete event systems owing to their compactness, resulting from the use of variables. In this paper, we propose a symbolic algorithm that efficiently synthesizes a supervisor for a plant modeled by an EFA and a specification defined by another EFA. The principle of the algorithm is to iteratively strengthen the guards of the plant EFA so that forbidden or blocking states become unreachable in the controlled plant. As a consequence of the algorithm, the controlled behavior is modeled by an EFA having the same structure as the plant EFA, having stronger guards and is shown to be maximally permissive. We illustrate our algorithm via a simple manufacturing example. Note to Practitioners-A compact way of modeling event-driven systems is to use state-variables, instead of an explicit enumeration of the states. This paper uses such a model for representing the system to be controlled as well as its desired behaviors, and develops a symbolic approach, that avoids explicit enumeration of the state-space, for control synthesis. The contribution is the symbolic computation of a safe (avoids reaching forbidden states) and nonblocking (avoids getting blocked at non final states) controller that is also maximal (permits all safe and nonblocking behaviors). The results are illustrated via a simple manufacturing system.