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Algorithms for leader selection in stochastically forced consensus networks
 IEEE Trans. Automat. Control
"... Abstract—We are interested in assigning a prespecified number of nodes as leaders in order to minimize the meansquare deviation from consensus in stochastically forced networks. This problem arises in several applications including control of vehicular formations and localization in sensor networ ..."
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Abstract—We are interested in assigning a prespecified number of nodes as leaders in order to minimize the meansquare deviation from consensus in stochastically forced networks. This problem arises in several applications including control of vehicular formations and localization in sensor networks. For networks with leaders subject to noise, we show that the Boolean constraints (which indicate whether a node is a leader) are the only source of nonconvexity. By relaxing these constraints to their convex hull we obtain a lower bound on the global optimal value. We also use a simple but efficient greedy algorithm to identify leaders and to compute an upper bound. For networks with leaders that perfectly follow their desired trajectories, we identify an additional source of nonconvexity in the form of a rank constraint. Removal of the rank constraint and relaxation of the Boolean constraints yields a semidefinite program for which we develop a customized algorithm wellsuited for large networks. Several examples ranging from regular lattices to random graphs are provided to illustrate the effectiveness of the developed algorithms. Index Terms—Alternating direction method of multipliers (ADMMs), consensus networks, convex optimization, convex relaxations, greedy algorithm, leader selection, performance bounds, semidefinite programming (SDP), sensor selection, variance amplification. I.
On Optimal Link Creation for Facilitation of Consensus in Social Networks
"... Abstract — We consider the problem of reaching consensus in a social network of agents described by the DeGroot model. We develop a measure for the efficiency with which consensus is reached, where the measure quantifies the transient behavior of public opinion around the consensus value. We then pr ..."
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Abstract — We consider the problem of reaching consensus in a social network of agents described by the DeGroot model. We develop a measure for the efficiency with which consensus is reached, where the measure quantifies the transient behavior of public opinion around the consensus value. We then propose an optimization problem that maximizes consensusreaching efficiency via the creation of new social links, subject to a total linkcreation budget. We employ the alternating direction method of multipliers, an algorithm wellsuited to large optimization problems, to find the optimal location and weights of the new links. We demonstrate the utility of our results through an example, where we observe that for a social network described by a regular graph the addition of new links leads to an augmented graph that resembles a smallworld network characterized by sparse longrange links. Index Terms — Alternating direction method of multipliers, consensus, DeGroot model, opinion dynamics, optimization, smallworld networks, social networks, sparsity, stochastic matrices. I.
1Algorithms for Leader Selection in Stochastically Forced Consensus Networks
"... We are interested in assigning a prespecified number of nodes as leaders in order to minimize the meansquare deviation from consensus in stochastically forced networks. This problem arises in several applications including control of vehicular formations and localization in sensor networks. For ne ..."
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We are interested in assigning a prespecified number of nodes as leaders in order to minimize the meansquare deviation from consensus in stochastically forced networks. This problem arises in several applications including control of vehicular formations and localization in sensor networks. For networks with leaders subject to noise, we show that the Boolean constraints (a node is either a leader or it is not) are the only source of nonconvexity. By relaxing these constraints to their convex hull we obtain a lower bound on the global optimal value. We also use a simple but efficient greedy algorithm to identify leaders and to compute an upper bound. For networks with leaders that perfectly follow their desired trajectories, we identify an additional source of nonconvexity in the form of a rank constraint. Removal of the rank constraint and relaxation of the Boolean constraints yields a semidefinite program for which we develop a customized algorithm wellsuited for large networks. Several examples ranging from regular lattices to random graphs are provided to illustrate the effectiveness of the developed algorithms. Index Terms Alternating direction method of multipliers, consensus networks, convex optimization, convex relaxations, greedy algorithm, leader selection, performance bounds, semidefinite programming, sensor selection, variance amplification. I.
Finitetime Convergence Policies in Statedependent Social Networks
"... Abstract — This paper addresses the problem of finitetime convergence in a social network for a political party or an association, modeled as a distributed iterative system with a graph dynamics chosen to mimic how people interact. It is firstly shown that, in this setting, finitetime convergence ..."
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Abstract — This paper addresses the problem of finitetime convergence in a social network for a political party or an association, modeled as a distributed iterative system with a graph dynamics chosen to mimic how people interact. It is firstly shown that, in this setting, finitetime convergence is achieved only when nodes form a complete network, and that contacting with agents with distinct opinions reduces to a half the necessary interconnections. Two novel strategies are presented that enable finitetime convergence, even for the case where each node only contacts the two closest neighbors. These strategies are of prime importance, for instance, in a company environment where agents can be motivated to reach faster conclusions. The performance of the proposed policies is evaluated through simulation, illustrating, in particular the finitetime convergence property. I.