I. Introduction
This paper deals with the finite-horizon covariance steering problem for discrete-time stochastic nonlinear (DTSN) systems. In particular, we consider the problem of steering the first moment (mean) and the second central moment (covariance) of the uncertain state of a DTSN system to desired quantities at a given (finite) terminal time. Nonlinear covariance steering problems can be formulated as PDE tracking problems which seek to minimize the distance of the probability density of the state, which evolves in space and time in accordance with the Fokker Planck partial differential equation (PDE), from a desired terminal density function [1]. The solution to the latter infinite-dimensional optimization problem, however, can be a very complex task in general. In this work, we will employ a more practical approach that relies on the solution of a sequence of linearized covariance steering problems which are in turn reduced to tractable convex optimization problems.