Optimal Input Calculation and Control for a Class of Timed Petri Nets under Marking Constraints

In this paper, a new control technique is developed for a class of Petri net subject to synchronization phenomena. Combined with dioids algebra, this work deals with the state feed-back control of TEGs under specifications expressed with linear marking constraints. The optimal input of TEGs is calculated and multiple controller design strategies based on the calculated optimal input are proposed to obtain an optimal or a sub-optimal controller, for the purpose of improving the throughput of the system. Some conditions for whether the control laws can be used are also discussed. The computed controller can be represented by a set of marked and timed places.