The Occupation Kernel Method for Nonlinear System Identification

TL;DR

This paper introduces the occupation kernel method, a novel approach for nonlinear system identification that embeds system trajectories into a reproducing kernel Hilbert space using Liouville operators and occupation kernels, enabling accurate and noise-robust parameter estimation.

Contribution

It develops a new framework combining occupation kernels and Liouville operators in RKHSs for nonlinear system identification, providing a novel data embedding and analysis technique.

Findings

Accurately identifies system parameters.

Demonstrates robustness to noise.

Provides a new theoretical foundation for system embedding.

Abstract

This manuscript presents a novel approach to nonlinear system identification leveraging densely defined Liouville operators and a new "kernel" function that represents an integration functional over a reproducing kernel Hilbert space (RKHS) dubbed an occupation kernel. The manuscript thoroughly explores the concept of occupation kernels in the contexts of RKHSs of continuous functions, and establishes Liouville operators over RKHS where several dense domains are found for specific examples of this unbounded operator. The combination of these two concepts allow for the embedding of a dynamical system into a RKHS, where function theoretic tools may be leveraged for the examination of such systems. This framework allows for trajectories of a nonlinear dynamical system to be treated as a fundamental unit of data for nonlinear system identification routine. The approach to nonlinear system identification is demonstrated to identify parameters of a dynamical system accurately, while also exhibiting a certain robustness to noise.