  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 is 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 the exponential stability of MPC.
It is proved that 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 in this paper.
