On the influencing net and forbidden state control of timed Petri nets with forced transitions

We discuss forbidden state feedback control design for real-time discrete event systems modeled by timed Petri nets. The firing time of a state-enabled transition lies in an interval which can be modified for controllable transitions. Once the upper bound is reached, the transition, controllable or uncontrollable, is forced to fire. We construct necessary and sufficient conditions for the control to satisfy forbidden state control objectives for the case of a timed marked graph. From these equations we derive what the influencing net looks like