Kernel Methods for the Approximation of Nonlinear Systems
For engineers and scientists dealing with complex nonlinear systems, this work provides a novel approach to model reduction that combines machine learning techniques with control theory.
The paper introduces a data-driven order reduction method for nonlinear control systems by leveraging kernel methods to lift the system into a high-dimensional feature space where balanced truncation is performed, resulting in a reduced-order model that captures essential input-output characteristics.
We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space where balanced truncation may be carried out implicitly. This leads to a nonlinear reduction map which can be combined with a representation of the system belonging to a reproducing kernel Hilbert space to give a closed, reduced order dynamical system which captures the essential input-output characteristics of the original model. Empirical simulations illustrating the approach are also provided.