A System Parameterization for Direct Data-Driven Estimator Synthesis

TL;DR

This paper proposes a new parameterization method for unknown LTI systems using noisy data, enabling direct data-driven estimator synthesis with H-infinity guarantees and providing insights into data consistency conditions.

Contribution

It introduces a novel parameterization that characterizes all systems consistent with data and derives conditions for exact system identification and estimator synthesis.

Findings

The parameterization exactly describes all systems compatible with data.

Verifiable conditions determine when the true system is identified.

Numerical experiments show improved estimator synthesis compared to existing methods.

Abstract

This paper introduces a novel parameterization to characterize unknown linear time-invariant systems using noisy data. The presented parameterization describes exactly the set of all systems consistent with the available data. We then derive verifiable conditions, when the consistency constraint reduces the set to the true system and when it does not have any impact. Furthermore, we demonstrate how to use this parameterization to perform a direct data-driven estimator synthesis with guarantees on the H_{\infty}-norm. Lastly, we conduct numerical experiments to compare our approach to existing methods.