  This paper considers the problem of steering the state distribution of a
nonlinear stochastic system from an initial Gaussian to a terminal distribution
with a specified mean and covariance, subject to probabilistic path
constraints. An algorithm is developed to solve this problem by iteratively
solving an approximate linearized problem as a convex program. This method,
which we call iterative covariance steering (iCS), is numerically demonstrated
by controlling a double integrator with quadratic drag force subject to
additive Brownian noise while satisfying probabilistic path constraints.
