Formal solution for the generalized mutual exclusion constraints problem in a class of timed Petri Nets

In this paper, we propose an analytical solution to the problem of Generalized Mutual Exclusion Constraints (GMECs) in a Network of Timed Event Graphs (NTEGs). The contribution of the paper lies in the development of a method to design control laws that satisfy these constraints across different paths in the graphs. Using Min-Plus dioid algebra, we employ algebraic techniques to express GMECs as weighted inequalities. The solution involves translating the constraints into Min- Plus linear equations that describe the behavior of NTEGs. We provide sufficient conditions for the existence of causal control laws, considering both the initial marking of the NTEGs and the parameters of the GMECs. To demonstrate the practical application of the approach, we include a case study that illustrates the effectiveness of the proposed control strategy.