  To address the issue of inaccurate distributions in practical stochastic
systems, a minimax linear-quadratic control method is proposed using the
Wasserstein metric. Our method aims to construct a control policy that is
robust against errors in an empirical distribution of underlying uncertainty,
by adopting an adversary that selects the worst-case distribution. The opponent
receives a Wasserstein penalty proportional to the amount of deviation from the
empirical distribution. A closed-form expression of the finite-horizon optimal
policy pair is derived using a Riccati equation. The result is then extended to
the infinite-horizon average cost setting by identifying conditions under which
the Riccati recursion converges to the unique positive semi-definite solution
to an algebraic Riccati equation. Our method is shown to possess several
salient features including closed-loop stability, and an out-of-sample
performance guarantee. We also discuss how to optimize the penalty parameter
for enhancing the distributional robustness of our control policy. Last but not
least, a theoretical connection to the classical $H_\infty$-method is
identified from the perspective of distributional robustness.
