Adaptive Robust Tracking Control with Active Learning for Linear Systems with Ellipsoidal Bounded Uncertainties

This article is concerned with the robust tracking control of linear uncertain systems, whose unknown system parameters and disturbances are bounded within ellipsoidal sets. We propose an adaptive robust control that can actively learn the ellipsoid sets. Particularly, our approach utilizes the ellipsoidal set-membership estimation in learning the ellipsoid sets, aiming at narrowing the uncertainty boundaries to reduce the conservativeness in robust control. To further improve the transient performance during the uncertainty learning, we enrich the information fed to the learning by maximizing the volume of the ellipsoid set. The maximized set volume stimulates the system to actively learn the uncertainties and leads to accelerated uncertainty reduction. We conduct numerical simulations to demonstrate the improvement of the proposed method.