Partial Order Control and Optimal Control of Discrete Event Systems modeled as Polynomial Dynamical Systems over Galois fields

In this paper, we propose computational methods for the synthesis of controllers for discrete event systems modeled by polynomial dynamical systems over finite Galois field. The control objectives are specified as order relations to be checked and as minimization of a given cost function over the states through the trajectories of the system. The control objectives are then synthesized using algebraic tools such as ideals, varieties and morphisms. The applications of these methods to the safety specification of a power transformer station controller is finally presented