Predictive Linear Online Tracking for Unknown Targets
Anastasios Tsiamis Aren Karapetyan Yueshan Li Efe C. Balta John Lygeros
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.