  We consider covariance control problems for nonlinear stochastic systems. Our
objective is to find an optimal control strategy to steer the state from an
initial distribution to a terminal one with specified mean and covariance. This
problem is considerably more complicated than previous studies on covariance
control for linear systems. We leverage a widely used technique - differential
dynamic programming - in nonlinear optimal control to achieve our goal. In
particular, we adopt the stochastic differential dynamic programming framework
to handle the stochastic dynamics. Additionally, to enforce the terminal
statistical constraints, we construct a Lagrangian and apply a primal-dual type
algorithm. Several examples are presented to demonstrate the effectiveness of
our framework.
