Minimal Interconnection Topology in Distributed Control Design

We propose and partially analyze a new model for determining the influence of a controller’s interconnection graph on closed-loop performance in distributed control design problems. Given a plant composed of dynamically uncoupled subsystems, we investigate the existence and properties of an optimal structured controller, when one of the weight matrices of a classical LQR cost function is topology-dependent. We also give some theoretical results as to the existence of "critical prices" at which adding supplementary edges becomes detrimental to closed-loop performance.

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