Prior Knowledge for System Identification with Linear and Nonlinear FIR Models

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This project shall investigate a new approach to linear and nonlinear system identification. It fuses classical methods with modern kernel-based machine learning ideas. The goal of this project is the development of a class of novel system identification methods for linear and nonlinear finite impulse response models. These are extremely flexible, inherently stable, output error models which are linear in their parameters. The key challenge is to automatically control the bias/variance tradeoff in spite of the huge number of nominal parameters/dimensions.In particular, various possibilities to incorporate prior knowledge on the shape of the impulse response via the regularization penalty term (or prior in terms of the Bayesian interpretation) shall be pursued extensively. This shall allow for gray-box modeling approaches with a smooth transition between different degrees of transparency from black to white, in contrast to the classical discrete classification proposed by Ljung for various popular model structures.Subgoal 1: Improvement of the performance and interpretability of linear regularized finite impulse response models. Subgoal 2: Transfer of many features from subgoal 1 to the nonlinear world via local model networks. A key insight while trying to transfer linear FIR models to nonlinear ones naively is, that the huge number of parameters becomes a huge number of dimensions. This issue is solved via a special feature of local model networks: the separation of input spaces for the validity functions and for the local models.