Contribution on the Control of Mixed Constrained Discrete Event Systems for a Flexible Workshop Application

This paper aims to extend the existing developed approaches for the control synthesis of state feedback control for the class of Timed Discrete Event Systems particularly its subclass represented by Timed Event Graphs. Accordingly, we introduce a new solving approach based on the Petri nets under the existence of mixed constraints. Capacity and time are both critical criteria that could sometimes evolve together and need to be respected at the same time for proper systems conduction, especially for industrial sensitive applications. In this sense, we look to compute suitable control laws in order to meet these critical specifications. Wherefore, we aim to satisfy sufficient conditions to ensure the respect of these restrictions. Based on the use of linear dioid algebra for the analytical modeling and on Petri nets for the graphical modeling, the general dynamical behavior of the system is described by linear Min-plus equations while the mixed constraints are represented by linear inequations.