Nonlinear Data-Driven Moment Matching in Reproducing Kernel Hilbert Spaces

The continuously increasing amount of noisy data demands the development of accurate and efficient models for analysis, modeling, and control. In this article, we propose a novel data-driven moment matching method which employs Tikhonov regularization in the Reproducing Kernel Hilbert Spaces (RKHSs). Specifically, considering a realistic scenario in which the system's plant is unknown and only noisy measured data are available, we provide an estimation of the moment of the unknown plant by solving a regularized optimization problem on RKHS. For, we first demonstrate that the estimation of the moment can be improved via tuning the regularization term, and further, we show under which condition the effect of the transient improves the performance of the estimation. Then, we construct a parameterized model characterized by a kernel-based output mapping. Finally, the proposed data-driven approach is validated and discussed by means of a DC-to-DC Cuk converter driven by a Van der Pol oscillator.