Data Informativity for Quadratic Stabilization under Data Perturbation

TL;DR

This paper introduces a unified framework for data informativity in quadratic stabilization that handles both system and measurement noise without restrictive assumptions, using data perturbation.

Contribution

It develops an extended matrix S-procedure lemma to analyze data perturbation, unifying existing noise models under a less restrictive approach.

Findings

Unified analysis of data informativity for control under noise.

Elimination of restrictive assumptions in measurement noise analysis.

Extension of the matrix S-procedure for data perturbation.

Abstract

Assessing data informativity, determining whether the measured data contains sufficient information for a specific control objective, is a fundamental challenge in data-driven control. In noisy scenarios, existing studies deal with system noise and measurement noise separately, using quadratic matrix inequalities. Moreover, the analysis of measurement noise requires restrictive assumptions on noise properties. To provide a unified framework without any restrictions, this study introduces data perturbation, a novel notion that encompasses both existing noise models. It is observed that the admissible system set with data perturbation does not meet preconditions necessary for applying the key lemma in the matrix S-procedure. Our analysis overcomes this limitation by developing an extended version of this lemma, making it applicable to data perturbation. Our results unify the existing analyses while eliminating the need for restrictive assumptions made in the measurement noise scenario.