Minimizing multistep-ahead prediction error for piecewise ARX model identification

This paper presents a new approach for piecewise auto-regressive with exogenous inputs (ARX) model identification by minimizing the multistep-ahead prediction error. A piecewise ARX model can approximate a nonlinear process within a wide operating range, and thus minimizing its long-term prediction error is of importance for the successful application of model predictive control (MPC). The traditional MPC relevant identification (MRI) methods rely on tuning a noise model with structures known a priori, but its application for the piecewise ARX model is non-trivial. Instead, we design an algorithm to directly minimize the multistep-ahead prediction error by solving a mixed-integer nonlinear program (MINLP) without incorporating a noise model. The proposed solution method is tested on datasets from a simulated fermenter and a real heat exchanger, respectively. The results show that our approach yields models with smaller prediction error than the compared method on both training and testing datasets.