Data Informativity for Quadratic Stabilization under Data Perturbation
For researchers in data-driven control, this provides a more general and less restrictive framework for assessing data informativity under noise.
This paper introduces 'data perturbation' as a unified noise model for data-driven control, and develops an extended matrix S-procedure lemma to analyze data informativity for quadratic stabilization without restrictive assumptions. The approach unifies existing analyses of system and measurement noise.
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.