Sparse add-on controller design: A Youla approach to system-level performance

Abstract: The performance of high-tech systems is often dictated by a few performance objectives shared among the many closed-loop controlled subsystems operating in the machine, such as synchronization, coordination, and alignment, which necessitates control methods that explicitly address them to achieve optimal performance. The aim of this paper is to introduce a framework that improves system performance through system-level controllers designed to be implemented as add-ons to the existing subsystem control structure. The developed method parametrizes all stabilizing system-level add-on controllers using the Youla framework, enabling a convex formulation of the sparse $\mathcal{H}_2$ synthesis problem. The result is a sparse add-on controller that achieves the optimal trade-off between combined performance and interconnection complexity, as demonstrated through numerical simulations.