Some notes on MPC relevant identification

This work studies MPC relevant identification. We will discuss the use of error criteria in parameter estimation where the identified model is used in model predictive control (MPC). Assume that the model error is dominated by the variance which is caused by the disturbance, we will show that a model estimated using a k-step-ahead prediction error criterion is not optimal for k-step-ahead prediction in MPC control. A normal one-step-ahead prediction error criterion will be optimal for parameter estimation. Therefore, for MPC relevant identification of linear processes, one-step-ahead prediction error criterion should be used for parameter estimation. Simulations will be used to illustrate the idea. The relevance of the result for industrial applications will be shown using industrial data.