Optimal Experimental Design for Uncertain Systems Based on Coupled Differential Equations

TL;DR

This paper develops an optimal experimental design framework for uncertain Kuramoto oscillator systems, aiming to reduce uncertainty in coupling strengths and improve control robustness through quantifying experimental impact.

Contribution

It introduces a novel approach to design experiments that effectively reduce parameter uncertainty in coupled differential equation models, specifically for the Kuramoto system.

Findings

Effective reduction of uncertainty in coupling parameters.

Enhanced robustness in controlling uncertain oscillator networks.

Quantitative assessment of experimental impact on system performance.

Abstract

We consider the optimal experimental design problem for an uncertain Kuramoto model, which consists of N interacting oscillators described by coupled ordinary differential equations. The objective is to design experiments that can effectively reduce the uncertainty present in the coupling strengths between the oscillators, thereby minimizing the cost of robust control of the uncertain Kuramoto model. We demonstrate the importance of quantifying the operational impact of the potential experiments in designing optimal experiments.