Feedback properties of model predictive control for max-plus-linear systems

This paper proposes design methods for model predictive control (MPC) approach for discrete event dynamical systems modelled by max-plus-linear (MPL) systems from the aspect of feedback properties. First, we show a design method for MPC for MPL systems with interval parameters which makes it possible to take account of robustness for parameter variations. We derive a range of MPC input vector for MPL systems when the system parameters of the MPL system vary within the given intervals. Secondly, we derive an equivalent MPC control law for MPL systems in terms of time function. The MPC control law over max-plus algebra might not satisfy causality when the state variables for MPL systems stand for time at which events occur. Hence, the results of the paper makes it possible to examine the feedback properties of the MPC control law over max-plus algebra.