|Model predictive control (MPC) has been developed for application in the process industry, where it has become a very popular advanced control strategy. A key advantage of MPC is that it is able to deal with constraints on the inputs and outputs. Usually MPC uses linear or nonlinear discrete-time models. Recently, MPC has been extended to various classes of hybrid systems, including max-plus linear systems and max-min-plus-scaling system. This will serve as the basis for our research.
Although in general a discrete-event system leads to a nonlinear description in conventional algebra, there exists a class of discrete-event systems that can be described by a model that is "linear" in the max-plus algebra. Typical examples of max-plus-linear systems are flexible manufacturing systems, telecommunication networks, traffic control systems, multiprocessor operating systems, and logistic systems. Max-min-plus-scaling systems are an extension of max-plus linear systems where minimization and scalar multiplication are included in the system description.
Most MPC problems for the hybrid systems mentioned above result in mixed integer linear or nonlinear programming problems, which may be hard to solve efficiently. In this project we focus on improving the efficiency of current MPC approaches for (switching) max-plus and max-min-plus-scaling systems. We propose to apply optimistic optimization to solve the MPC optimization problems. Given finite computational resources such as CPU time, optimistic optimization explores the feasible space to propose an action the performance of which is as close as possible to the optimal solution, based on the information about the previously observed evaluations and the knowledge of the local smoothness properties of the objective function. In this way efficient solution approaches for solving MPC problems for max-plus and max-min-plus-scaling systems will be developed.