Nonlinear System Identification with Orthonormal Basis Functions

• Applicant: Professor Dr.-Ing. Oliver Nelles
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 567641303

This proposal investigates different linear and nonlinear system identification approaches utilizing orthonormal basis function (OBF) models. While models with output or state feedback are widely researched and applied in linear as well as nonlinear system identification, there is still a lack of research on OBF models. Recently, the most simple type of OBF models, i.e., finite impulse response (FIR) models, have become more popular due to the introduction of new regularization strategies. However, other OBF types, e.g. Laguerre or Kautz models, are still neglected in research. This proposal aims to fill this research gap by investigating OBFs and their relationship to regularized FIR. Key advantages of these models are: (i) output error structure, (ii) inherent stability, and (iii) easy adaptability. However, they also have one severe drawback: Due to the lack of feedback flexibility, these models require many parameters to describe long impulse responses. To compensate for the lacking feedback flexibility, the structure and choice of the hyperparameters play a crucial role. Via an appropriate hyperparameter scheme, this drawback can be overcome. Therefore, this proposal focuses on developing, extending, and improving strategies for hyperparameter incorporation and their inclusion in the estimation procedure.Four major challenges will be addressed in this proposal. First, novel techniques for FIR models will be developed and analyzed that automate choices regarding model structure within the regularization schemes. Theses structural choices can be e.g. time delays, model order, and existence of direct feedthrough. Second, inherently stable model structures will be used for adaptation. They allow the incorporation of prior knowledge (gray-box) via regularization and automatically carry out a tradeoff between regularization strength and forgetting factor. Third, the properties of regularized FIR and more generalized OBF models (like Laguerre and Kautz) are currently not well understood and will be studied thoroughly. Fourth, many of the investigated strategies are extended to nonlinear modeling approaches via local model networks.

• DFG Programme: Research Grants