Maximum Likelihood Estimation in Data-Driven Modeling and Control

TL;DR

This paper introduces a maximum likelihood framework for data-driven modeling and control that effectively handles noisy data, improving model accuracy and control performance in noisy environments.

Contribution

It develops a maximum likelihood estimator for data-driven models, incorporating data compression and noise estimation, enhancing existing methods for noisy data scenarios.

Findings

Improved system identification with less restrictive assumptions.

Enhanced predictive control performance under high noise levels.

Demonstrated effectiveness on large datasets with unknown noise levels.

Abstract

Recently, various algorithms for data-driven simulation and control have been proposed based on the Willems' fundamental lemma. However, when collected data are noisy, these methods lead to ill-conditioned data-driven model structures. In this work, we present a maximum likelihood framework to obtain an optimal data-driven model, the signal matrix model, in the presence of output noise. Data compression and noise level estimation schemes are also proposed to apply the algorithm efficiently to large datasets and unknown noise level scenarios. Two approaches in system identification and receding horizon control are developed based on the derived optimal estimator. The first one identifies a finite impulse response model. This approach improves the least-squares estimator with less restrictive assumptions. The second one applies the signal matrix model as the predictor in predictive control. The control performance is shown to be better than existing data-driven predictive control algorithms, especially under high noise levels. Both approaches demonstrate that the derived estimator provides a promising framework to apply data-driven algorithms to noisy data.