Experiment design for MPC relevant identification

The bias and variance properties of identified models depend on various factors including the input spectrum. These properties of an estimated model have to be shaped in such a way that the resulting model is commensurate with the controller. This paper presents a few results on experiment design for Model Predictive Controllers. It is important to minimize multi step ahead predictions, as opposed to one step ahead prediction errors, if Model Predictive Controllers are used. An optimal weighting on the model error for multi step ahead prediction errors is derived. Using this weighting, optimal input spectra are derived for the open loop systems.