Gaussian Process-Based Prediction and Control of Hammerstein-Wiener Systems
This addresses a specific limitation in existing frameworks for structured nonlinear systems, making it an incremental but practical contribution for control engineering applications.
The paper tackles data-driven prediction and control of Hammerstein-Wiener systems by developing physics-informed Gaussian process models that handle output nonlinearities without requiring basis function dictionaries, demonstrating superior performance compared to black-box Gaussian process models in numerical results.
This work investigates data-driven prediction and control of Hammerstein-Wiener systems using physics-informed Gaussian process models. Data-driven prediction algorithms have been developed for structured nonlinear systems based on Willems' fundamental lemma. However, existing frameworks cannot treat output nonlinearities and require a dictionary of basis functions for Hammerstein systems. In this work, an implicit predictor structure is considered, leveraging the multi-step-ahead ARX structure for the linear part of the model. This implicit function is learned by Gaussian process regression with kernel functions designed from Gaussian process priors for the nonlinearities. The linear model parameters are estimated as hyperparameters by assuming a stable spline hyperprior. The implicit Gaussian process model provides explicit output prediction by optimizing selected optimality criteria. The model is also applied to receding horizon control with the expected control cost and chance constraint satisfaction guarantee. Numerical results demonstrate that the proposed prediction and control algorithms are superior to black-box Gaussian process models.