Online Regulation of Unstable Linear Systems from a Single Trajectory

In this paper, we study online regulation of partially unknown (and possibly unstable) linear systems. In order to avoid the popular assumption of having access to an initial stabilizing controllers in learning algorithms, we propose the Data-Guided Regulator (DGR) synthesis that regulates the underlying states of an unknown linear model through generating informative data. We also introduce the notion of "regularizability" for a linear system that is of independent interest and provides a unique perspective on the geometry of data-guided regulation. Finally, we discuss an example involving online regulation of the (open-loop unstable) X-29 aircraft.