Modelling and control of discrete event systems using switching max-plus-linear systems

In this paper we consider the modelling and control of discrete event systems using switching max-plus-linear systems. In switching max-plus-linear systems we can switch between different modes of operation. In each mode the discrete event system is described by a max-plus-linear state space model with different system matrices for each mode. The switching allows us to change the structure of the system, to break synchronization and to change the order of events. We will give some examples of this type of systems.We define the model predictive control design problem for this type of discrete event system, and we show that solving this problem in general leads to a mixed integer optimization problem.