Semiparametric Kernel Ridge Regression: Incorporating Structural Prior Knowledge

Kernel methods are popular in data-driven control owing to their analytical convenience and the availability of explicit error bounds. However, traditional kernel-based techniques have difficulties incorporating prior structural knowledge about target functions, despite the advantages that many real-world engineering applications benefit from integrating partial information about system dynamics, such as in system identification tasks. Therefore, this paper introduces a semiparametric kernel ridge regression framework. The proposed method constructs a regressor by combining known basis functions with nonparametric elements belonging to a reproducing kernel Hilbert space. We present a closed-form solution for this regression approach, establish an error bound for the resulting model, and validate its performance through simulations, showing that it outperforms both standard kernel interpolants and least-squares methods when combined with a hyperparameter optimization procedure.