Informativity for Data-driven Prediction

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.