Federated Nonlinear System Identification

TL;DR

This paper develops federated learning methods for nonlinear system identification, providing theoretical guarantees and experimental validation on physical systems, showing improved convergence with more clients.

Contribution

It introduces a federated approach for nonlinear system identification with theoretical convergence guarantees and experimental validation on real-analytic dynamical systems.

Findings

Federated learning improves convergence as the number of clients increases.

The convergence rate depends on the feature map choice, affecting excitation and performance.

Experimental results validate theoretical predictions on physical nonlinear systems.

Abstract

We consider federated learning of linearly-parameterized nonlinear systems. We establish theoretical guarantees on the effectiveness of federated nonlinear system identification compared to centralized approaches, demonstrating that the convergence rate improves as the number of clients increases. Although the convergence rates in the linear and nonlinear cases differ only by a constant, this constant depends on the feature map $\phi$, which can be carefully chosen in the nonlinear setting to increase excitation and improve performance. We experimentally validate our theory in physical settings where client devices are driven by i.i.d. control inputs and control policies exhibiting i.i.d. random perturbations, ensuring non-active exploration. Experiments use trajectories from nonlinear dynamical systems characterized by real-analytic feature functions, including polynomial and trigonometric components, representative of physical systems including pendulum and quadrotor dynamics. We analyze the convergence behavior of the proposed method under varying noise levels and data distributions. Results show that federated learning consistently improves convergence of any individual client as the number of participating clients increases.