Covariance control for discrete-time stochastic linear systems with incomplete state information

This work deals with a finite-horizon covariance control problem for discrete-time stochastic linear systems with incomplete state information subject to constraints. We show that under the assumption that the class of admissible control policies for this stochastic optimal control problem is comprised of sequences of non-anticipative (causal) control laws that can be expressed as linear combinations of the past and present output measurements of the system, then the covariance control problem can be reduced to a finite-dimensional, deterministic nonlinear program with a convex performance index. In addition, we show that the nonlinear program can be associated with a convex program via a simple relaxation technique that allows us to express the non-convex matrix equality constraint induced by the boundary condition on the terminal state covariance as a positive semi-definite (convex) constraint.