The Occupation Kernel Method for Nonlinear System Identification [article]

Joel A. Rosenfeld, Benjamin Russo, Rushikesh Kamalapurkar, Taylor T. Johnson
2021 arXiv   pre-print
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
more » ... is 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.
arXiv:1909.11792v3 fatcat:tnk7sz2izfeo5iusua7xj2smtq