Colloquium Mathematics - Dr. H. van der Waarde

Title: Data-driven control: informative data and how to acquire it

Abstract:

This talk concerns the design of control laws for an unknown dynamical system on the basis of measured data. As an important prerequisite to this design problem, we will first tackle the question of when data contain sufficient information for data-driven control. To do so, we will define a suitable notion of informative data. We then characterize the informativity of data for different control problems such as stabilization and optimal control. We treat both the settings in which data are exact, and corrupted by bounded noise. In the case of exact data, our results reveal that stabilization can be performed with less data samples than optimal control. In the case of noisy data, our investigations lead to an interesting byproduct in the form of a generalization of Yakubovich' S-lemma. In addition to studying data informativity, we also propose new data-driven control methods. These methods are based on linear matrix equations and inequalities, and enable the tractible computation of controllers from finite (informative) data sets. As our last problem, we will investigate how to generate informative data by appropriately selecting the system's inputs. This can be done using a result called Willems' fundamental lemma, which we will discuss during the talk.