Kernel Based Transfer Function Estimation with Enhanced Prior Knowledge

The systems and control community has a long history of successful applications in engineering domains, traditionally making use of domain-specific knowledge and dynamic properties of systems. Machine learning has specialised in classification and regression from a black-box perspective, often using a Bayesian approach. Combining both offers opportunities, especially in efficiently optimising model structures and complexities for estimating models of measured dynamic systems, while imposing (interpretable) properties to these models.

This talk discusses the data-driven modelling of Linear Time-Invariant (LTI) systems with Gaussian Processes (GP) regression. First, GP regression in general, and Time domain and frequency domain expressions of LTI systems are reviewed. Then, relevant system-specific properties, s.a. causality and stability are encoded in kernels, used as prior knowledge for estimation purposes. Care is given to visual interpretations of this prior knowledge in the spectral domain. Finally, recent results are shared on the estimation of the more challenging situation, where the systems are lightly damped. The combination of the non-parametric local rational model (LRM) estimator with the GP regression approach is proposed.