On the pole selection for ℋ∞-optimal decentralized control

We consider the problem of finding decentralized controllers to optimize an ℋ∞-norm. This can be cast as a convex optimization problem when certain conditions are satisfied, but it is an infinite-dimensional problem that in general cannot be addressed with existing methods. Given a choice of basis, Q-parametrization can be used to approach the original problem with a finite-dimensional one, whose basis coefficients could be found by an SDP. In this paper, we improve the basis selection phase in three stages. First, we use the poles from the optimal centralized controller as to suggest those for an initial basis. Second, we use sparse optimization methods to effectively select poles from many candidates. Finally, we use a Taylor approximation which allows us to formulate another SDP that systematically adjusts the poles and the coefficients to improve the closed-loop performance.