Title: Finite Time Adaptive Stabilization of LQ Systems,
Abstract: Stabilization of linear systems with unknown dynamics is a canonical problem
in adaptive control. Since the lack of knowledge of system parameters can cause
it to become destabilized, an adaptive stabilization procedure is needed prior
to regulation. Therefore, the adaptive stabilization needs to be completed in
finite time. In order to achieve this goal, asymptotic approaches are not very
helpful. There are only a few existing non-asymptotic results and a full
treatment of the problem is not currently available.
In this work, leveraging the novel method of random linear feedbacks, we
establish high probability guarantees for finite time stabilization. Our
results hold for remarkably general settings because we carefully choose a
minimal set of assumptions. These include stabilizability of the underlying
system and restricting the degree of heaviness of the noise distribution. To
derive our results, we also introduce a number of new concepts and technical
tools to address regularity and instability of the closed-loop matrix.