Balanced Reduction of Nonlinear Control Systems in Reproducing Kernel Hilbert Space

TL;DR

This paper presents a new data-driven nonlinear control system reduction method using reproducing kernel Hilbert spaces, enabling effective model simplification while preserving key input-output behaviors.

Contribution

It introduces a novel kernel-based reduction technique that implicitly performs balanced truncation in a high-dimensional feature space for nonlinear systems.

Findings

Effective reduction of nonlinear systems demonstrated

Captures essential input-output characteristics

Applicable to high-dimensional feature spaces

Abstract

We introduce a novel 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.