32nd IEEE Conference on Decision and Control

We study the inverse problem of reproducing partially known second-order statistics of a linear time invariant system by the least number of possible input disturbance channels.This can be formulated as a rank minimization problem, and for its solution, we employ a convex relaxation based on the nuclear norm.The resulting optimization problem can be cast as a semi-definite program and solved efficiently using generalpurpose solvers for small-and medium-size problems.In this paper, we focus on issues and techniques that are pertinent to large-scale systems.We bring in a re-parameterization which transforms the problem into a form suitable for the alternating direction method of multipliers.Furthermore, we show that each iteration of this algorithm amounts to solving a system of linear equations, an eigenvalue decomposition, and a singular value thresholding.An illustrative example is provided to demonstrate the effectiveness of the developed approach.