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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.
In the Dance Studio: An Art and Engineering Exploration of Human Flocking ∗†
"... Abstract. Flock Logic was developed as an art and engineering project to explore how the feedback laws used to model flocking translate when applied by dancers. The artistic goal was to create choreographic tools that leverage multiagent system dynamics with designed feedback and interaction. The e ..."
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Abstract. Flock Logic was developed as an art and engineering project to explore how the feedback laws used to model flocking translate when applied by dancers. The artistic goal was to create choreographic tools that leverage multiagent system dynamics with designed feedback and interaction. The engineering goal was to provide insights and design principles for multiagent systems, such as human crowds, animal groups and robotic networks, by examining what individual dancers do and what emerges at the group level. We describe our methods to create dance and investigate collective motion. We analyze video of an experiment in which dancers moved according to simple rules of cohesion and repulsion with their neighbors. Using the prescribed interaction protocol and tracked trajectories, we estimate the timevarying graph that defines who is responding to whom. We compute status of nodes in the graph and show the emergence of leaders. We discuss results and further directions.
IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 1 Transfer
"... functions in consensus systems with higherorder dynamics and external inputs ..."
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functions in consensus systems with higherorder dynamics and external inputs
1Joint Centrality Distinguishes Optimal Leaders in Noisy Networks
"... We study the performance of a network of agents tasked with tracking an external unknown signal in the presence of stochastic disturbances and under the condition that only a limited subset of agents, known as leaders, can measure the signal directly. We investigate the optimal leader selection prob ..."
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We study the performance of a network of agents tasked with tracking an external unknown signal in the presence of stochastic disturbances and under the condition that only a limited subset of agents, known as leaders, can measure the signal directly. We investigate the optimal leader selection problem for a prescribed maximum number of leaders, where the optimal leader set minimizes total system error defined as steadystate variance about the external signal. In contrast to previously established greedy algorithms for optimal leader selection, our results rely on an expression of total system error in terms of properties of the underlying network graph. We demonstrate that the performance of any given set of leaders depends on their influence as determined by a new graph measure of centrality of a set. We define the joint centrality of a set of nodes in a network graph such that a leader set with maximal joint centrality is an optimal leader set. In the case of a single leader, we prove that the optimal leader is the node with maximal information centrality. In the case of multiple leaders, we show that the nodes in the optimal leader set balance high information centrality with a coverage of the graph. For special cases of graphs, we solve explicitly for optimal leader sets. We illustrate with examples. I.
1Topology Design for Optimal Network Coherence
"... Abstract—We consider a network topology design problem in which an initial undirected graph underlying the network is given and the objective is to select a set of edges to add to the graph to optimize the coherence of the resulting network. We show that network coherence is a submodular function of ..."
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Abstract—We consider a network topology design problem in which an initial undirected graph underlying the network is given and the objective is to select a set of edges to add to the graph to optimize the coherence of the resulting network. We show that network coherence is a submodular function of the network topology. As a consequence, a simple greedy algorithm is guaranteed to produce near optimal edge set selections. We also show that fast rank one updates of the Laplacian pseudoinverse using generalizations of the ShermanMorrison formula and an accelerated variant of the greedy algorithm can speed up the algorithm by several orders of magnitude in practice. These allow our algorithms to scale to network sizes far beyond those that can be handled by convex relaxation heuristics. I.
InNetwork Leader Selection for Acyclic Graphs
"... Abstract—We study the problem of leader selection in leaderfollower multiagent systems that are subject to stochastic disturbances. This problem arises in applications such as vehicle formation control, distributed clock synchronization, and distributed localization in sensor networks. We pose a ..."
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Abstract—We study the problem of leader selection in leaderfollower multiagent systems that are subject to stochastic disturbances. This problem arises in applications such as vehicle formation control, distributed clock synchronization, and distributed localization in sensor networks. We pose a new leader selection problem called the innetwork leader selection problem. Initially, an arbitrary node is selected to be a leader, and in all consequent steps the network must have exactly one leader. The agents must collaborate to find the leader that minimizes the variance of the deviation from the desired trajectory, and they must do so within the network using only communication between neighbors. To develop a solution for this problem, we first show a connection between the leader selection problem and a class of discrete facility location problems. We then leverage a previously proposed selfstabilizing facility location algorithm to develop a selfstabilizing innetwork leader selection algorithm for acyclic graphs. I.
Information Centrality and Ordering of Nodes for Accuracy in Noisy DecisionMaking Networks
 ACCEPTED IN THE IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 2015
"... This paper considers a network of stochastic evidence accumulators, each represented by a driftdiffusion model accruing evidence towards a decision in continuous time by observing a noisy signal and by exchanging information with other units according to a fixed communication graph. These network ..."
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This paper considers a network of stochastic evidence accumulators, each represented by a driftdiffusion model accruing evidence towards a decision in continuous time by observing a noisy signal and by exchanging information with other units according to a fixed communication graph. These network dynamics model distributed sequential hypothesis testing as well as collective decision making. We prove the relationship between the location of each unit in the graph and its certainty as measured by the inverse of the variance of its state. Under mild connectivity assumptions, we show that only in balanced directed graphs do the node variances remain within a bounded constant from the minimum possible variance. We then prove that, for these digraphs, node ranking based on certainty is governed by information centrality, which depends on the notion of effective resistance suitably generalized to directed graphs. Our results, which describe the certainty of each unit as a function of the structural properties of the graph, can guide the selection of leaders in problems that involve the observation of noisy external signals by a cooperative multiagent network.