Model Predictive Control for Productions Systems Based on Max-plus Algebra

Among the state-space description of discrete vent systems, the max-plus algebra is known as one of the effective approach. This paper proposes a model predictive control (MPC) design method based on the max-plus algebra. Several studies related to these topics have been done so far under the constraints that system parameters are constant. However, in practical systems such as production systems, it is common and sometimes inevitable that system parameters vary by each event. Therefore, it is of worth to design a new MPC controller taking account of adjustable system parameters. In this paper, we formulate system parameters as adjustable ones, and they are solved by a linear programing method. Since MPC determines optimal control input considering future reference signals, the controller can be more robust and the operation cost can be reduced. Finally, the proposed method is applied to a production system with three machines, and the effectiveness of the proposed method is verified through a numerical simulation.