  Precise control under uncertainty requires a good understanding and
characterization of the noise affecting the system. This paper studies the
problem of steering state distributions of dynamical systems subject to
partially known uncertainties. We model the distributional uncertainty of the
noise process in terms of Wasserstein ambiguity sets, which, based on recent
results, have been shown to be an effective means of capturing and propagating
uncertainty through stochastic LTI systems. To this end, we propagate the
distributional uncertainty of the state through the dynamical system, and,
using an affine feedback control law, we steer the ambiguity set of the state
to a prescribed, terminal ambiguity set. We also enforce distributionally
robust CVaR constraints for the transient motion of the state so as to reside
within a prescribed constraint space. The resulting optimization problem is
formulated as a semi-definite program, which can be solved efficiently using
standard off-the-shelf solvers. We illustrate the proposed
distributionally-robust framework on a quadrotor landing problem subject to
wind turbulence.
