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

arXiv: https://arxiv.org/abs/2109.04742 · HTML: https://mlsanity.com/paper/2109.04742/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2021.

## Built on by (most cited first, 1 of 1)

- [Data-Driven Prediction and Control of Hammerstein-Wiener Systems with Implicit Gaussian Processes](https://mlsanity.com/paper/2501.15849/) (2025)

## Abstract (arXiv)

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.