Optimal Petri Net Monitor Design

The classical partition of the event set into controllable and uncontrollable events from supervisory control theory is replaced by introducing the concept of control and observation cost of an event. This leads naturally to consider an optimal control problem for a given logical control specification. On the other hand, if we consider a timed model a performance optimization may be considered as well. Here the case of generalized mutual exclusion constraint is considered for a Petri net plant. It has been shown that a constraint of this kind may be enforced via a monitor place. In this paper we propose an integer programming approach to synthesize the optimal monitor so as to minimize a given cost that represent a trade-off between the controller cost and cycle time of the closed loop net.