PLS-based model predictive control relevant identification: PLS-PH algorithm

Control-relevant identification produces a model by minimizing a cost function that is commensurate with the control cost function. This paper focuses on model predictive control (MPC); thus, a multi-step ahead prediction error cost function is minimized. Numerical optimization algorithms such as Levenberg-Marquardt can be used to minimize the non-linear identification cost function provided the identification data set is not ill-conditioned. A PLS-based line search numerical optimization approach denoted PLS-PH is proposed to tackle the minimization of the identification cost function in case the identification data set is ill-conditioned. PLS-PH fits a MIMO linear model to an identification data set that may be ill-conditioned. Two chemical processes are identified to compare predictive performance of models obtained using Least Squares, Levenberg-Marquardt, and PLS-PH. The two examples show that the models fitted with PLS-PH outperform the other models if the identification data set is ill-conditioned.