  We consider control of dynamical systems through the lens of competitive
analysis. Most prior work in this area focuses on minimizing regret, that is,
the loss relative to an ideal clairvoyant policy that has noncausal access to
past, present, and future disturbances. Motivated by the observation that the
optimal cost only provides coarse information about the ideal closed-loop
behavior, we instead propose directly minimizing the tracking error relative to
the optimal trajectories in hindsight, i.e., imitating the clairvoyant policy.
By embracing a system level perspective, we present an efficient
optimization-based approach for computing follow-the-clairvoyant (FTC) safe
controllers. We prove that these attain minimal regret if no constraints are
imposed on the noncausal benchmark. In addition, we present numerical
experiments to show that our policy retains the hallmark of competitive
algorithms of interpolating between classical $\mathcal{H}_2$ and
$\mathcal{H}_\infty$ control laws - while consistently outperforming regret
minimization methods in constrained scenarios thanks to the superior ability to
chase the clairvoyant.
