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32
NewtonRaphson consensus for distributed convex optimization
 In CDC and European Control Conference
, 2011
"... Abstract — We study the problem of unconstrained distributed optimization in the context of multiagents systems subject to limited communication connectivity. In particular we focus on the minimization of a sum of convex cost functions, where each component of the global function is available only ..."
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Abstract — We study the problem of unconstrained distributed optimization in the context of multiagents systems subject to limited communication connectivity. In particular we focus on the minimization of a sum of convex cost functions, where each component of the global function is available only to a specific agent and can thus be seen as a private local cost. The agents need to cooperate to compute the minimizer of the sum of all costs. We propose a consensuslike strategy to estimate a NewtonRaphson descending update for the local estimates of the global minimizer at each agent. In particular, the algorithm is based on the separation of timescales principle and it is proved to converge to the global minimizer if a specific parameter that tunes the rate of convergence is chosen sufficiently small. We also provide numerical simulations and compare them with alternative distributed optimization strategies like the Alternating Direction Method of Multipliers and the Distributed Subgradient Method. Index Terms — distributed optimization, convex optimization, consensus algorithms, multiagent systems, NewtonRaphson methods I.
Controllability Metrics, Limitations and Algorithms for Complex Networks
"... Abstract — This paper studies the problem of controlling stable and symmetric complex networks, that is, the joint problem of selecting a set of control nodes and of designing a control input to drive a network to a target state. We adopt the smallest eigenvalue of the controllability Gramian as met ..."
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Abstract — This paper studies the problem of controlling stable and symmetric complex networks, that is, the joint problem of selecting a set of control nodes and of designing a control input to drive a network to a target state. We adopt the smallest eigenvalue of the controllability Gramian as metric for the controllability degree of a network, as it identifies the energy needed to accomplish the control task. In the first part of the paper we characterize tradeoffs between the control energy and the number of control nodes, based on the network topology and weights. Our bounds show for instance that, if the number of control nodes is constant, then the control energy increases exponentially with the number of network nodes. Consequently, despite the classic controllability notion, few nodes cannot in practice arbitrarily symmetric control complex networks. In the second part of the paper we propose a distributed openloop strategy with performance guarantees for the control of complex networks. In our strategy we select control nodes based on network partitioning, and we design the control input based on optimal and distributed control techniques. For our control strategy we show that the control energy depends on the controllability properties of the clusters and on their coupling strength, and it is independent of the network dimension. I.
Synchronization in Complex Networks of Phase Oscillators: A Survey
, 2014
"... The emergence of synchronization in a network of coupled oscillators is a fascinating subject of multidisciplinary research. This survey reviews the vast literature on the theory and the applications of complex oscillator networks. We focus on phase oscillator models that are widespread in realworl ..."
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The emergence of synchronization in a network of coupled oscillators is a fascinating subject of multidisciplinary research. This survey reviews the vast literature on the theory and the applications of complex oscillator networks. We focus on phase oscillator models that are widespread in realworld synchronization phenomena, that generalize the celebrated Kuramoto model, and that feature a rich phenomenology. We review the history and the countless applications of this model throughout science and engineering. We justify the importance of the widespread coupled oscillator model as a locally canonical model and describe some selected applications relevant to control scientists, including vehicle coordination, electric power networks, and clock synchronization. We introduce the reader to several synchronization notions and performance estimates. We propose analysis approaches to phase and frequency synchronization, phase balancing, pattern formation, and partial synchronization. We present the sharpest known results about synchronization in networks of homogeneous and heterogeneous oscillators, with complete or sparse interconnection topologies, and in finitedimensional and infinitedimensional settings. We conclude by summarizing the limitations of existing analysis methods and by highlighting some directions for future research.
Finitetime average consensus based protocol for distributed estimation over awgn channels
 In Proc. of the 50th IEEE Conference on Decision and Control (CDC
, 2011
"... Finitetime average consensus based protocol for distributed estimation over AWGN ..."
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Finitetime average consensus based protocol for distributed estimation over AWGN
Information Weighted Consensus Filters and their Application in Distributed Camera Networks
"... Abstract—Due to their high faulttolerance and scalability to large networks, consensusbased distributed algorithms have recently gained immense popularity in the sensor networks community. Large scale camera networks are a special case. In a consensusbased state estimation framework, multiple nei ..."
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Abstract—Due to their high faulttolerance and scalability to large networks, consensusbased distributed algorithms have recently gained immense popularity in the sensor networks community. Large scale camera networks are a special case. In a consensusbased state estimation framework, multiple neighboring nodes iteratively communicate with each other, exchanging their own local information about each target’s state with the goal of converging to a single state estimate over the entire network. However, the state estimation problem becomes challenging when some nodes have limited observability of the state. In addition, the consensus estimate is suboptimal when the crosscovariances between the individual state estimates across different nodes are not incorporated in the distributed estimation framework. The crosscovariance is usually neglected because the computational and bandwidth requirements for its computation become unscalable for a large network. These limitations can be overcome by noting that, as the state estimates at different nodes converge, the information at each node becomes correlated. This fact can be utilized to compute the optimal estimate by proper weighting of the prior state and measurement information. Motivated by this idea, we propose informationweighted consensus algorithms for distributed maximum a posteriori parameter estimation, and their extension to the informationweighted consensus filter (ICF) for state estimation. We compare the performance of the ICF with existing consensus algorithms analytically, as well as experimentally by considering the scenario of a distributed camera network under various operating conditions. I.
Novel results on slow coherency in consensus and power networks
 in European Control Conference, Zürich
, 2013
"... Abstract — We revisit the classic slow coherency and area aggregation approach to model reduction in power networks. The slow coherency approach is based on identifying sparsely and densely connected areas of a network, within which all generators swing coherently. A timescale separation and singul ..."
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Abstract — We revisit the classic slow coherency and area aggregation approach to model reduction in power networks. The slow coherency approach is based on identifying sparsely and densely connected areas of a network, within which all generators swing coherently. A timescale separation and singular perturbation analysis then results in a reduced loworder system, where coherent areas are collapsed into aggregate variables. Here, we study the application of slow coherency and area aggregation to firstorder consensus systems and secondorder power system swing dynamics. We unify different theoretic approaches and ideas found throughout the literature, we relax some technical assumptions, and we extend existing results. In particular, we provide a complete analysis of the secondorder swing dynamics – without restrictive assumptions on the system damping. Moreover, we identify the reduced aggregate models as generalized first or secondorder Laplacian flows with multiple time constants, aggregate damping and inertia matrices, and possibly adverse interactions. I.
Controllability Metrics and Algorithms for Complex Networks
"... This paper studies the problem of controlling complex networks, that is, the joint problem of selecting a set of control nodes and of designing a control input to steer the network to a target state. For this problem (i) we propose a metric to quantify the difficulty of the control problem as a func ..."
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This paper studies the problem of controlling complex networks, that is, the joint problem of selecting a set of control nodes and of designing a control input to steer the network to a target state. For this problem (i) we propose a metric to quantify the difficulty of the control problem as a function of the required control energy, (ii) we derive bounds based on the system dynamics (network topology and weights) to characterize the tradeoff between the control energy and the number of control nodes, and (iii) we propose a distributed strategy with performance guarantees for the control of complex networks. In our strategy we select control nodes by relying on network partitioning, and we design the control input by leveraging optimal and distributed control techniques. Our findings show for instance that (i) if the number of control nodes is constant, then the control energy increases exponentially with the number of the network nodes, (ii) if the number of control nodes is a fixed fraction of the network nodes, then certain networks can be controlled with constant energy independently of the network dimension, and (iii) clustered networks may be easier to control because, for sufficiently many control nodes, the control energy depends only on the controllability properties of the clusters and on their coupling strength. We validate our results with examples from power networks, social networks, and epidemics spreading. I.
RESISTANCEBASED PERFORMANCE ANALYSIS OF THE CONSENSUS ALGORITHM OVER GEOMETRIC GRAPHS∗
"... Abstract. The performance of the linear consensus algorithm is studied by using a Linear Quadratic (LQ) cost. The objective is to understand how the communication topology influences this algorithm. This is achieved by exploiting an analogy between Markov Chains and electrical resistive networks. In ..."
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Abstract. The performance of the linear consensus algorithm is studied by using a Linear Quadratic (LQ) cost. The objective is to understand how the communication topology influences this algorithm. This is achieved by exploiting an analogy between Markov Chains and electrical resistive networks. Indeed, this permits to uncover the relation between the LQ performance cost and the average effective resistance of a suitable electrical network and, moreover, to show that, if the communication graph fulfils some local properties, then its behavior can be approximated by that of a grid, which is a graph whose associated LQ cost is wellknown. Key words. Multiagent systems, consensus algorithm, distributed averaging, largescale graphs AMS subject classifications. 68R10, 90B10, 94C15, 90B18, 05C50 1. Introduction. The
On aggregate control of clustered consensus networks
 in American Control Conference (ACC), 2015. IEEE
"... Abstract — We address a consensus control problem for networks that have multiple dense areas with sparse interconnection structure. The sparsity pattern in such networks naturally gives rise to a timescale separation in its dynamics, whereby nodes inside an area synchronize over a fast timescal ..."
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Abstract — We address a consensus control problem for networks that have multiple dense areas with sparse interconnection structure. The sparsity pattern in such networks naturally gives rise to a timescale separation in its dynamics, whereby nodes inside an area synchronize over a fast timescale while the areas themselves synchronize over a slow timescale. Our goal is to design statefeedback controllers at the network nodes that predominantly shape the closedloop response of the slow dynamics. The specific design objective in this case is posed as maximizing the speed of convergence of the slow dynamics. A sparsitypromoting graph design problem is formulated for achieving this purpose. A critical observation is that every areacoordinator needs to design only one aggregate control law to satisfy this objective for the slow system. Applying results from singular perturbation theory, we show that when these individual controllers are implemented on the actual network model, the closedloop response is close to that obtained from the approximate models, provided that the clustering is strong. The design procedure is demonstrated by a simulation example. Index Terms — Largescale systems; Singular perturbation; Consensus networks; Sparse networks; Area aggregation
Making NonCentralized a Model Predictive Control Scheme by Using Distributed Smith Dynamics?
"... (email: {j.barreiro135, geoband, nquijano} @ uniandes.edu.co) Abstract: This paper proposes a non–centralized Model Predictive Control (MPC) scheme for a system comprised by several subsystems. Operational constraints for each sub–system are considered as well as a single coupled constraint on th ..."
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(email: {j.barreiro135, geoband, nquijano} @ uniandes.edu.co) Abstract: This paper proposes a non–centralized Model Predictive Control (MPC) scheme for a system comprised by several subsystems. Operational constraints for each sub–system are considered as well as a single coupled constraint on the control inputs that models a limitation of the resource supplied by the controller. If the underlying optimization problem is of largescale nature, traditional MPC suffers from computational burden issues. A cause of this problem is the requirement of having centralized information to guarantee that the computed control actions satisfy the coupled constraint. In this work, a traditional MPC is made non–centralized by means of a strategy based on distributed population dynamics. The proposed methodology divides the problem into several local MPC controllers that coordinate their decisions by using a communication network without the need of a centralized scheme. It is proved that this methodology provides an optimal solution that satisfies both the operational constraints of each sub–system, and the coupled constraint of the control signals. Finally, the proposed method is compared with a traditional centralized MPC in an industrial problem that involves several continuously stirred tank reactors.