In this paper, we study the problem of online tracking in linear control
systems, where the objective is to follow a moving target. Unlike classical
tracking control, the target is unknown, non-stationary, and its state is
revealed sequentially, thus, fitting the framework of online non-stochastic
control. We consider the case of quadratic costs and propose a new algorithm,
called predictive linear online tracking (PLOT). The algorithm uses recursive
least squares with exponential forgetting to learn a time-varying dynamic model
of the target. The learned model is used in the optimal policy under the
framework of receding horizon control. We show the dynamic regret of PLOT
scales with $\mathcal{O}(\sqrt{TV_T})$, where $V_T$ is the total variation of
the target dynamics and $T$ is the time horizon. Unlike prior work, our
theoretical results hold for non-stationary targets. We implement PLOT on a
real quadrotor and provide open-source software, thus, showcasing one of the
first successful applications of online control methods on real hardware.

研究在线跟踪线性控制系统中的问题，目标是追踪一个移动目标，提出了一种新的算法 PLOT，该算法使用递归最小二乘法和指数遗忘来学习目标的时变动态模型，并在前向视界控制框架下使用学到的模型。展示了 PLOT 的动态遗憾量与目标动力学的总变化量成正比，理论结果适用于非平稳目标，并在真实四旋翼上实施 PLOT，提供了开源软件，因此展示了在线控制方法在真实硬件上的成功应用之一。