Informativity for Data-driven Prediction

TL;DR

This paper investigates weaker data conditions than persistency of excitation for predicting outputs of unknown LTI systems, introducing informativity concepts and algorithms for unique prediction.

Contribution

It formalizes the notion of informativity for data-driven prediction and provides conditions and algorithms for unique output prediction without full system identification.

Findings

Unique output prediction is possible without full system identification.

Sufficient conditions for informativity are established.

Algorithms for computing the output trajectory are developed.

Abstract

In this work we examine the problem of data-driven prediction. That is, given a LTI system with unknown dynamics, we wish to use data collected from the system to predict the system's output response to a given sequence of known inputs. Current methods for predicting require strong conditions on the data such as persistency of excitation. We examine this problem with the goal of finding weaker conditions that still enable prediction. We approach the problem from the data informativity perspective and formally define the notion of informativity for unique prediction. We provide sufficient conditions for informativity for unique prediction and design algorithms to compute the unique output trajectory of the unknown system given known inputs. We demonstrate the results with a numerical example showing that unique output prediction is possible without being able to uniquely identify the unknown data-generating system.