On the Regret Analysis of Online LQR Control with Predictions

In this paper, we study the dynamic regret of online linear quadratic regulator (LQR) control with time-varying cost functions and disturbances. We consider the case where a finite look-ahead window of cost functions and disturbances are available at each stage. The online control algorithm studied in this paper falls into the category of model predictive control (MPC) with a particular choice of terminal costs to ensure exponential stability. It is proved that, when predictions are accurate, the regret of such an online algorithm decays exponentially fast with the length of predictions. The impact of inaccurate prediction on disturbances is also investigated, showing that errors of long-term predictions have an exponentially diminishing effect on dynamic regret.