Closed-loop control of constrained discrete event systems: application to a networked automation system

In this paper, we are interested in the design of closed-loop control laws to satisfy a set of temporal constraints in discrete event systems modeled by timed event graphs (TEGs). The dynamic behavior of the TEG is represented by a system of linear equations in Max-Plus algebra. Temporal constraints are imposed on some paths of the TEG and are expressed by a set of Max-Plus linear inequalities. The proposed approach is applied to the control of a networked automation producer/consumer system under a temporal constraint. The temporal constraint to be satisfied is imposed on the response time of the considered networked automation system (NAS). The calculated control laws are causal feedbacks and can be represented by monitor places connected to the NAS model.