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Leader selection in directed networks


N. K. Dhingra, M. Colombino, M.R. Jovanovic

IEEE Conference on Decision and Control, Las Vegas, pp. 2715 - 2720

We study the problem of leader selection in directed consensus networks. In this problem, certain ‘leader’ nodes in a consensus network are equipped with absolute information about their state. This corresponds to diagonally strengthening a dynamical generator given by the negative of a directed graph Laplacian. We provide a necessary and sufficient condition for the stabilization of directed consensus networks via leader selection and form regularized H2 and H∞ optimal problem leader selection problems. We draw on recent results that establish the convexity of the H2 and H∞ norms for structured decentralized control of positive systems and identify sparse sets of leaders by imposing an l1 penalty on the vector of leader weights. This allows us to develop a method that simultaneously assigns leader weights and selects a limited number of leaders. We use proximal gradient and subgradient method to solve the optimization problems and provide examples to illustrate our developments.


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% Autogenerated BibTeX entry
@InProceedings { DhiCol:2016:IFA_5617,
    author={N. K. Dhingra and M. Colombino and M.R. Jovanovic},
    title={{Leader selection in directed networks}},
    booktitle={IEEE Conference on Decision and Control},
    pages={2715 -- 2720},
    address={Las Vegas},
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