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Design of optimal sparse feedback gains via the alternating direction method of multipliers
 IEEE Trans. Automat. Control
"... Abstract—We design sparse and block sparse feedback gains that minimize the variance amplification (i.e., the norm) of distributed systems. Our approach consists of two steps. First, we identify sparsity patterns of feedback gains by incorporating sparsitypromoting penalty functions into the optim ..."
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Cited by 33 (8 self)
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Abstract—We design sparse and block sparse feedback gains that minimize the variance amplification (i.e., the norm) of distributed systems. Our approach consists of two steps. First, we identify sparsity patterns of feedback gains by incorporating sparsitypromoting penalty functions into the optimal control problem, where the added terms penalize the number of communication links in the distributed controller. Second, we optimize feedback gains subject to structural constraints determined by the identified sparsity patterns. In the first step, the sparsity structure of feedback gains is identified using the alternating direction method of multipliers, which is a powerful algorithm wellsuited to large optimization problems. This method alternates between promoting the sparsity of the controller and optimizing the closedloop performance, which allows us to exploit the structure of the corresponding objective functions. In particular, we take advantage of the separability of the sparsitypromoting penalty functions to decompose the minimization problem into subproblems that can be solved analytically. Several examples are provided to illustrate the effectiveness of the developed approach. Index Terms—Alternating direction method of multipliers (ADMM), communication architectures, continuation methods, minimization, optimization, separable penalty functions, sparsitypromoting optimal control, structured distributed design. I.
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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Cited by 12 (3 self)
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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.
Information Centrality and Optimal Leader Selection in Noisy Networks
 IN: PROC. IEEE CONFERENCE ON DECISION AND CONTROL. IEEE
, 2013
"... We consider the leader selection problem in which a system of networked agents, subject to stochastic disturbances, uses a decentralized coordinated feedback law to track an unknown external signal, and only a limited number of agents, known as leaders, can measure the signal directly. The optima ..."
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Cited by 9 (2 self)
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We consider the leader selection problem in which a system of networked agents, subject to stochastic disturbances, uses a decentralized coordinated feedback law to track an unknown external signal, and only a limited number of agents, known as leaders, can measure the signal directly. The optimal leader selection minimizes the total system error by minimizing the steadystate variance about the external signal, equivalent to an H2 norm of the linear stochastic network dynamics. Efficient greedy algorithms have been proposed in the literature for similar optimal leader selection problems. In contrast, we seek systematic solutions. We prove that the single optimal leader is the node in the network graph with maximal information centrality. In the case of two leaders, we prove that the optimal pair maximizes a joint centrality, which depends on the information centrality of each leader and how well the pair covers the graph. We apply these results to solve explicitly for the optimal single leader and the optimal pair of leaders in special classes of network graphs. To generalize we compute joint centrality for m leaders.
Rearranging trees for robust consensus
 IN PROC. 50TH IEEE CONF. ON DECISION AND CONTROL
, 2011
"... In this paper, we use the H2 norm associated with a communication graph to characterize the robustness of consensus to noise. In particular, we restrict our attention to trees, and by systematic attention to the effect of local changes in topology, we derive a partial ordering for undirected trees ..."
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Cited by 3 (1 self)
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In this paper, we use the H2 norm associated with a communication graph to characterize the robustness of consensus to noise. In particular, we restrict our attention to trees, and by systematic attention to the effect of local changes in topology, we derive a partial ordering for undirected trees according to the H2 norm. Our approach for undirected trees provides a constructive method for deriving an ordering for directed trees. Further, our approach suggests a decentralized manner in which trees can be rearranged in order to improve their robustness.
on UF performance
 Water Res
"... of leaderfollower networks in directed trees and lattices ..."
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of leaderfollower networks in directed trees and lattices
On identifying sparse representations of consensus networks
 in Proc. 3rd IFAC Wkshp Distrib. Estim. Control Netw. Syst
, 2012
"... Abstract: We consider the problem of identifying optimal sparse graph representations of dense consensus networks. The performance of the sparse representation is characterized by the global performance measure which quantifies the difference between the output of the sparse graph and the output of ..."
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Abstract: We consider the problem of identifying optimal sparse graph representations of dense consensus networks. The performance of the sparse representation is characterized by the global performance measure which quantifies the difference between the output of the sparse graph and the output of the original graph. By minimizing the sum of this performance measure and a sparsitypromoting penalty function, the alternating direction method of multipliers identifies sparsity structures that strike a balance between the performance measure and the number of edges in the graph. We then optimize the edge weights of sparse graphs over the identified topologies. Two examples are provided to illustrate the utility of the developed approach.
Graphtheoretic bounds on disturbance propagation in interconnected linear dynamical networks
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 2014
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Emergent Collective Behavior in MultiAgent Systems: An Evolutionary Perspective
"... The study of collective behavior involves the analysis of interactions among a set of agents that yield collective outcomes at the level of the group. The behavior is said to be emergent when it cannot be understood simply as the sum of its constituent parts. Further, grouplevel outcomes can in tur ..."
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Cited by 2 (0 self)
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The study of collective behavior involves the analysis of interactions among a set of agents that yield collective outcomes at the level of the group. The behavior is said to be emergent when it cannot be understood simply as the sum of its constituent parts. Further, grouplevel outcomes can in turn influence individual interactions. The complexity of this interplay makes the study of emergence challenging and exciting. This dissertation is focused on the study of emergent collective behavior from the perspective of evolution. Evolution is a simple yet powerful algorithm, which when acting on interacting entities in a dynamic environment, yields an array of fascinating behavior as manifest in the natural world. Natural collectives display a wide variety of cooperative behavior and have evolved to efficiently manage the inherent tradeoff between robust behavior and adaptability to dynamic environments. These properties have motivated the design of bioinspired algorithms for sensing and decisionmaking in robotic collectives. In this work, we study the evolutionary mechanisms for cooperation and tradeoff management in biological collectives, with a focus on four related topics: replicatormutator dynamics, collective migration, collective pursuit
A family of algorithms for computing consensus about node state from network data
 PLoS Computational Biology
"... Biological and social networks are composed of heterogeneous nodes that contribute differentially to network structure and function. A number of algorithms have been developed to measure this variation. These algorithms have proven useful for applications that require assigning scores to individual ..."
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Cited by 2 (1 self)
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Biological and social networks are composed of heterogeneous nodes that contribute differentially to network structure and function. A number of algorithms have been developed to measure this variation. These algorithms have proven useful for applications that require assigning scores to individual nodes–from ranking websites to determining critical species in ecosystems–yet the mechanistic basis for why they produce good rankings remains poorly understood. We show that a unifying property of these algorithms is that they quantify consensus in the network about a node’s state or capacity to perform a function. The algorithms capture consensus by either taking into account the number of a target node’s direct connections, and, when the edges are weighted, the uniformity of its weighted indegree distribution (breadth), or by measuring net flow into a target node (depth). Using data from communication, social, and biological networks we find that that how an algorithm measures consensus–through breadth or depth – impacts its ability to correctly score nodes. We also observe variation in sensitivity to source biases in interaction/adjacency matrices: errors arising from systematic error at the node level or direct manipulation of network connectivity by nodes. Our results indicate that the breadth algorithms, which are derived from information theory, correctly score nodes (assessed using independent data) and are robust to errors. However, in cases where nodes ‘‘form opinions’ ’ about other nodes using indirect information, like reputation, depth algorithms, like Eigenvector Centrality, are required. One caveat is that Eigenvector Centrality is not robust to error unless
Biometric Identification
 Communication of the ACM
, 2000
"... of sparse communication graphs in consensus networks ..."
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of sparse communication graphs in consensus networks