  In this paper, we propose a minimax linear-quadratic control method to
address the issue of inaccurate distribution information in practical
stochastic systems. To construct a control policy that is robust against errors
in an empirical distribution of uncertainty, our method is to adopt an
adversary, which selects the worst-case distribution. To systematically adjust
the conservativeness of our method, the opponent receives a penalty
proportional to the amount, measured with the Wasserstein metric, of deviation
from the empirical distribution. In the finite-horizon case, using a Riccati
equation, we derive a closed-form expression of the unique optimal policy and
the opponent's policy that generates the worst-case distribution. This result
is then extended to the infinite-horizon setting by identifying conditions
under which the Riccati recursion converges to the unique positive
semi-definite solution to an associated algebraic Riccati equation (ARE). The
resulting optimal policy is shown to stabilize the expected value of the system
state under the worst-case distribution. We also discuss that our method can be
interpreted as a distributional generalization of the $H_\infty$-method.
