Open loop controllers to solve the disturbance decoupling problem for max-plus linear systems

This paper presents the new investigations on the disturbance decoupling problem (DDP) in the geometric control of max-plus linear systems. Due to the monotone nondecreasing property of max-plus linear systems, a modified disturbance decoupling problem (MDDP) is defined and an optimal controller to solve the MDDP is obtained using a prefilter mapping by taking the disturbances into account. Moreover, this paper presents a necessary and sufficient condition such that the same optimal controller for the MDDP can be used to solve the DDP for max-plus linear systems. When the necessary and sufficient condition is not satisfied, a new disturbance mapping is developed in order to guarantee the solvability of the DDP by the same optimal controller for the MDDP. The main results of this paper are illustrated by using a timed event graph model of a manufacturing network.