Model predictive control with discrete actuators: Theory and application

Despite the presence of discrete actuators in many industrial processes, model predictive control (MPC) theory typically considers only continuous actuators, which requires discrete decisions to be removed from the MPC layer. However, if discrete inputs are chosen optimally, process performance may be greatly improved, and thus, discrete decisions should be treated directly in MPC theory. In this paper, we develop the idea that discrete actuators can be added to MPC theory without major modification, i.e., results established with sufficient generality for standard MPC with continuous actuators hold also for MPC with discrete actuators. First, we show that standard exponential stability for suboptimal MPC can be extended without modification to cover discrete actuators by avoiding restrictive assumptions about the geometry of the control set. Then, we prove stability results for tracking MPC applied to a time-varying periodic system. Finally, we demonstrate these results with two example systems.