M.C. Rotkowitz and N.C. Martins
On the Number of Iterations to the Closest Quadratically Invariant Information Constraint
Proceedings of the 18th IFAC World Congress, pp. 9115-9120, August 2011.

Abstract

Quadratic invariance is a condition which has been shown to allow for optimal decentralized control problems to be cast as convex optimization problems. The condition relates the constraints that the decentralization imposes on the controller to the structure of the plant. Recent work considered the problem of finding the closest subset and superset of the decentralization constraint which are quadratically invariant when the original problem is not. It was shown that this can itself be cast as a convex problem for the case where the controller is subject to delay constraints between subsystems, but that this fails when we only consider sparsity constraints on the controller. For that case, an algorithm was developed that finds the closest superset in a fixed number of steps, and it was shown to converge in n^2 iterations, where n is the number of subsystems. This paper studies the algorithm further and shows that it actually converges in log n iterations.