Design of input for data-driven simulation with Hankel and Page matrices

TL;DR

This paper presents new methods for designing informative input signals for data-driven simulation, considering both noise-free and noisy data, with a focus on Hankel and Page matrix representations to improve predictive accuracy.

Contribution

It introduces weaker excitation conditions for noise-free data and formulates an input design problem for noisy data using a maximum likelihood estimator with a Bayesian perspective.

Findings

Weaker excitation conditions for noise-free data are established.

Input design significantly improves predictive accuracy in numerical examples.

Hankel and Page matrices are effectively used in the input design process.

Abstract

The paper deals with the problem of designing informative input trajectories for data-driven simulation. First, the excitation requirements in the case of noise-free data are discussed and new weaker conditions, which assume the simulated input to be known in advance, are provided. Then, the case of noisy data trajectories is considered and an input design problem based on a recently proposed maximum likelihood estimator is formulated. A Bayesian interpretation is provided, and the implications of using Hankel and Page matrix representations are demonstrated. Numerical examples show the impact of the designed input on the predictive accuracy.