Regret Analysis of Online LQ Control Using Trajectory Prediction and Tracking

Abstract

We propose a new framework for solving online linear quadratic (LQ) control problems with time-varying cost matrices that are known only up to the current time or over a short preview window. Our framework involves using revealed cost matrices to predict the unknown optimal trajectory, and then using a tracking controller to drive the system towards this prediction. We adopted the notion of dynamic regret to measure and bound the resulting quality of control decisions with and without system disturbances, and present a constructive tracking controller design approach based on deadbeat control in a lifted space. Our analysis reveals that the regret of controllers designed using this proposed ..