On model predictive control for max-plus-linear systems

The max-plus-linear (MPL) system is a state-space description for a certain class of discrete-event-systems that are linear in max-plus algebra. The several researches on control design for MPL systems have been reported from the viewpoint of an analogy between the MPL systems and the traditional linear state-space representations. The design method for model predictive control (MPC) for MPL systems has been studied in the context of such researches. Two main approaches have been proposed for MPC for MPL systems. One approach is based on the extended linear complementarity problem (ELCP), and another approach is based on the greatest subsolution. This paper considers the relation between these approaches, and compares several features in these approaches.