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In this paper we demonstrate how certain structured feedback gainsnecessarily emerge as the optimal controller gains in two linear optimalcontrol formulations for multi-agent systems. We consider the cases of linearoptimal synchronization and linear optimal centroid stabilization. In theformer problem, the considered cost functional integrates squaredsynchronization error and input, and in the latter, the considered costfunctional integrates squared sum of the states and input. Our approach is toview the structures in the feedback gains in terms of a static output feedbackwith suitable output matrices and to relate this fact with the optimal controlformulations. We show that the two considered problems are special cases of amore general case in which the optimal feedback to a linear quadratic regulatorproblem with cost functionals integrating squared outputs and inputs is astatic output feedback. A treatment in this light leads to a very simple andgeneral solution which significantly generalizes a recent result for the linearoptimal synchronization problem. We illustrate the general problem in ageometric light.

Structured Optimal Feedback in Multi-Agent Systems: A Static Output Feedback Perspective