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In this paper, we present a new control policy parametrization for thefinite-horizon covariance steering problem for discrete-time Gaussian linearsystems (DTGLS) which can reduce the latter stochastic optimal control problemto a tractable optimization problem. The covariance steering problem seeks fora feedback control policy that will steer the state covariance of a DTGLS to adesired positive definite matrix in finite time. We consider two differentformulations of the covariance steering problem, one with hard terminal LMIconstraints (hard-constrained covariance steering) and another one with softterminal constraints in the form of a terminal cost which corresponds to thesquared Wasserstein distance between the actual terminal state (Gaussian)distribution and the desired one (soft-constrained covariance steering). Wepropose a solution approach that relies on the affine disturbance feedbackparametrization for both problem formulations. We show that this particularparametrization allows us to reduce the hard-constrained covariance steeringproblem into a semi-definite program (SDP) and the soft-constrained covariancesteering problem into a difference of convex functions program(DCP). Finally,we show the advantages of our approach over other covariance steeringalgorithms in terms of computational complexity and computation time by meansof theoretical analysis and numerical simulations.

Covariance Control of Discrete-Time Gaussian Linear Systems Using Affine Disturbance Feedback Control Policies