Stock Reduction for Timed Event Graphs Based on Output Feedback

In timed event graphs (TEG), stock represents the number of tokens present in the system. It is very similar to work-in-process for manufacturing systems. In general, when choosing a feedback controller, a compromise is sought between fastness of the system and stock size. The classical choice in the (max, +) literature consists in reducing the stock as much as possible without delaying the output. In this paper, the constraint is weakened: the response of the controlled system to a specific, predefined reference input w must be as fast as the one of the uncontrolled system, but may be slower for other inputs. In return, lower stock is expected. After formally defining this new controller, its performance in terms of stock is compared with the one of the classical controller. This last part relies heavily on second order theory for TEG.