|The class of discrete-event systems essentially consists of man-made systems that contain a finite number of resources (such as machines, communications channels, or processors) that are shared by several users (such as product types, information packets, or jobs) all of which contribute to the achievement of some common goal (the assembly of products, the end-to-end transmission of a set of information packets, or a parallel computation).
In general, models that describe the behavior of a discrete-event system are nonlinear in conventional algebra. However, there is a class of discrete-event systems the max-plus-linear discrete-event systems that can be described by a model that is linear in the max-plus algebra, which has maximization and addition as its basic operations. Max-plus-linear systems can be characterized as the class of discrete-event systems in which only synchronization and no concurrency or choice occurs. In [van den Boom & De Schutter, International Journal of Control, 2004] a model predictive control (MPC) algorithm was derived for stochastic max-plus-linear systems. Such systems have attracted lots of attentions lately.
This project aims at developing more efficient methods for computing performance criteria and other properties of stochastic max-plus-linear systems so as to decrease the computation time and complexity. By achieving this aim, we can improve the current MPC algorithms and other model-based control methods for stochastic max-plus-linear systems, as well as extensions such as stochastic max-min-plus-scaling (MMPS) and switching max-plus-linear (SMPL) systems.