[2501.15849] Data-Driven Prediction and Control of Hammerstein-Wiener Systems with Implicit Gaussian Processes

Electrical Engineering and Systems Science > Systems and Control arXiv:2501.15849 (eess) [Submitted on 27 Jan 2025 (v1), last revised 2 Mar 2026 (this version, v2)] Title:Data-Driven Prediction and Control of Hammerstein-Wiener Systems with Implicit Gaussian Processes Authors:Mingzhou Yin, Matthias A. Müller View a PDF of the paper titled Data-Driven Prediction and Control of Hammerstein-Wiener Systems with Implicit Gaussian Processes, by Mingzhou Yin and Matthias A. M\"uller View PDF HTML (experimental) Abstract:This work investigates data-driven prediction and control of Hammerstein-Wiener systems using physics-informed Gaussian process (GP) models that encode the block-oriented model structure. Data-driven prediction algorithms have been developed for structured nonlinear systems based on Willems' fundamental lemma. However, existing frameworks do not apply to output nonlinearities in Wiener systems and rely on a finite-dimensional dictionary of basis functions for Hammerstein systems. In this work, an implicit predictor structure is considered, leveraging the linearity for the dynamical part of the model. This implicit function is learned by GP regression, utilizing carefully designed structured kernel functions from linear model parameters and GP priors for the nonlinearities. Virtual derivative points are added to the regression by expectation propagation to encode monotonicity information of the nonlinearities. The linear model parameters are estimated as hyperparam...