Adaptive Model Predictive Control for Max-plus Linear Systems Taking Account of Feedback Properties

The max-plus algebra is an algebraic system in which the max operation is addition and the plus operation is multiplication. The max-plus-linear (MPL) system is a state-space description/or a certain class of discrete-event-systems that are linear in the max-plus algebra. Recently, a model predictive control (MPC) method for the MPL systems has been proposed with the help of the analogy with the traditional state-space descriptions in the modern control theory. However, in practical situations, system parameters frequently change widely. So, it is desirable that the control systems have functions to tune system parameters adaptively. Therefore, this paper tries to extend the MPC for MPL systems in terms of time function to an adaptive ones in order to take account of feedback properties. The proposed adaptive MPC is designed by corporating a parameter identification method based on the greatest subsolution for linear equations with the MPC for MPL systems in terms of time function.