# Data informativity: a new perspective on data-driven analysis and control

## TL;DR

This paper introduces a new framework for data-driven analysis and control that relaxes the need for persistently exciting data, showing that some problems can be solved with less informative data than previously thought.

## Contribution

The paper develops a framework to analyze data informativity beyond persistency of excitation, providing necessary and sufficient conditions for various data-driven control and analysis tasks.

## Key findings

- Persistency of excitation is not always necessary for data-driven analysis.
- Some control problems can be addressed with less informative data.
- Persistently exciting data is essential only for certain system identification tasks.

## Abstract

The use of persistently exciting data has recently been popularized in the context of data-driven analysis and control. Such data have been used to assess system theoretic properties and to construct control laws, without using a system model. Persistency of excitation is a strong condition that also allows unique identification of the underlying dynamical system from the data within a given model class. In this paper, we develop a new framework in order to work with data that are not necessarily persistently exciting. Within this framework, we investigate necessary and sufficient conditions on the informativity of data for several data-driven analysis and control problems. For certain analysis and design problems, our results reveal that persistency of excitation is not necessary. In fact, in these cases data-driven analysis/control is possible while the combination of (unique) system identification and model-based control is not. For certain other control problems, our results justify the use of persistently exciting data as data-driven control is possible only with data that are informative for system identification.