Model predictive control relevant identification using partial least squares for building modeling

A dynamic model is a crucial part when dealing with the Model Predictive Controller (MPC). Very often a Prediction Error Method (PEM) framework is chosen for identification/modeling. In this framework one-step ahead prediction errors are minimized. In contrast, we examine a multi-step ahead prediction error cost function which satisfies the needs of the MPC for having a good prediction on a prediction horizon. Least Squares (LS) are probably the most often used tool in a variety of optimization algorithms. In case of ill-conditioned data due to e.g. co-linearity, the Ordinary LS (OLS) fail and provide biased estimate. We adapt an approach known in econometric, chemistry and biometrics, namely Partial Least Squares (PLS) and introduce an algorithm which combines the PLS and multi-step ahead algorithm. The proposed algorithm is then tested and verified. We show that for cases where the data suffer from collinearity and a proposed combined multi-step ahead identification with PLS is used, the results are better than in case of using standard multi-step ahead method. As a case study, we show a practical example, an identification and modeling of the Czech Technical University building, where we demonstrate, that the introduced multi-step ahead identification method has a better performance, than the standard one-step ahead predictions.