On the solution of Max-plus linear equations with application on the control of TEGs

In this paper, a method is proposed for generating solutions for linear Max-plus equations from a given solution. We have called this method as “Primal method”. The solutions generated by the Primal method have useful properties in the context of control of Timed Event Graph (TEG). In order to illustrate an application of the method, we present a sufficient condition for solving a feedback control problem for a TEG, based on the notion of “Equivalent System”. We can show that the desired feedback matrix is a solution of a Max-plus affine equation, which can be transformed into a linear one, and therefore the Primal method can be applied.