From Nonlinear Identification to Linear Parameter Varying Models: Benchmark Examples
For researchers in nonlinear system identification and control, this provides a practical bridge from nonlinear to LPV models, but the contribution is incremental as it builds on existing LFR and LPV frameworks.
The paper presents a systematic method to embed nonlinear fractional representation models into linear parameter-varying (LPV) models, enabling data-driven scheduling variable selection and avoiding measurement noise issues. The approach is demonstrated on two nonlinear benchmark examples.
Linear parameter-varying (LPV) models form a powerful model class to analyze and control a (nonlinear) system of interest. Identifying a LPV model of a nonlinear system can be challenging due to the difficulty of selecting the scheduling variable(s) a priori, which is quite challenging in case a first principles based understanding of the system is unavailable. This paper presents a systematic LPV embedding approach starting from nonlinear fractional representation models. A nonlinear system is identified first using a nonlinear block-oriented linear fractional representation (LFR) model. This nonlinear LFR model class is embedded into the LPV model class by factorization of the static nonlinear block present in the model. As a result of the factorization a LPV-LFR or a LPV state-space model with an affine dependency results. This approach facilitates the selection of the scheduling variable from a data-driven perspective. Furthermore the estimation is not affected by measurement noise on the scheduling variables, which is often left untreated by LPV model identification methods. The proposed approach is illustrated on two well-established nonlinear modeling benchmark examples.