  We consider the problem of tracking an adversarial state sequence in a linear
dynamical system subject to adversarial disturbances and loss functions,
generalizing earlier settings in the literature. To this end, we develop three
techniques, each of independent interest. First, we propose a
comparator-adaptive algorithm for online linear optimization with movement
cost. Without tuning, it nearly matches the performance of the optimally tuned
gradient descent in hindsight. Next, considering a related problem called
online learning with memory, we construct a novel strongly adaptive algorithm
that uses our first contribution as a building block. Finally, we present the
first reduction from adversarial tracking control to strongly adaptive online
learning with memory. Summarizing these individual techniques, we obtain an
adversarial tracking controller with a strong performance guarantee even when
the reference trajectory has a large range of movement.
