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Communication Constraints in the Average Consensus Problem
, 2007
"... The interrelationship between control and communication theory is becoming of fundamental importance in many distributed control systems, such as the coordination of a team of autonomous agents. In such a problem, communication constraints impose limits on the achievable control performance. We cons ..."
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Cited by 81 (19 self)
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The interrelationship between control and communication theory is becoming of fundamental importance in many distributed control systems, such as the coordination of a team of autonomous agents. In such a problem, communication constraints impose limits on the achievable control performance. We consider as instance of coordination the consensus problem. The aim of the paper is to characterize the relationship between the amount of information exchanged by the agents and the rate of convergence to the consensus. We show that timeinvariant communication networks with circulant symmetries yield slow convergence if the amount of information exchanged by the agents does not scale well with their number. On the other hand, we show that randomly timevarying communication networks allow very fast convergence rates. We also show that, by adding logarithmic quantized data links to timeinvariant networks with symmetries, control performance significantly improves with little growth of the required communication effort.
Finitetime convergent gradient flows with applications to network consensus
 Automatica
"... This paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function. Extending recent results on nonsmooth stability analysis, we characterize their asymptotic convergence properties and identify conditions that guarantee finitetime convergence. We d ..."
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Cited by 66 (5 self)
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This paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function. Extending recent results on nonsmooth stability analysis, we characterize their asymptotic convergence properties and identify conditions that guarantee finitetime convergence. We discuss the application of the results to the design of multiagent coordination algorithms, paying special attention to their scalability properties. Finally, we consider network consensus problems and show how the proposed nonsmooth gradient flows achieve the desired coordination task in finite time.
Distributed function calculation via linear iterations in the presence of malicious agents – part I: Attacking the network,” in
 Proc. of the American Control Conference,
, 2008
"... AbstractGiven a network of interconnected nodes, each with its own value (such as a measurement, position, vote, or other data), we develop a distributed strategy that enables some or all of the nodes to calculate any arbitrary function of the node values, despite the actions of malicious nodes in ..."
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Cited by 66 (5 self)
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AbstractGiven a network of interconnected nodes, each with its own value (such as a measurement, position, vote, or other data), we develop a distributed strategy that enables some or all of the nodes to calculate any arbitrary function of the node values, despite the actions of malicious nodes in the network. Our scheme assumes a broadcast model of communication (where all nodes transmit the same value to all of their neighbors) and utilizes a linear iteration where, at each timestep, each node updates its value to be a weighted average of its own previous value and those of its neighbors. We consider a node to be malicious or faulty if, instead of following the predefined linear strategy, it updates its value arbitrarily at each timestep (perhaps conspiring with other malicious nodes in the process). We show that the topology of the network completely characterizes the resilience of linear iterative strategies to this kind of malicious behavior. First, when the network contains 2f or fewer vertexdisjoint paths from some node xj to another node xi, we provide an explicit strategy for f malicious nodes to follow in order to prevent node xi from receiving any information about xj 's value. Next, if node xi has at least 2f + 1 vertexdisjoint paths from every other (nonneighboring) node, we show that xi is guaranteed to be able to calculate any arbitrary function of all node values when the number of malicious nodes is f or less. Furthermore, we show that this function can be calculated after running the linear iteration for a finite number of timesteps (upper bounded by the number of nodes in the network) with almost any set of weights (i.e., for all weights except for a set of measure zero).
Distributed Function Calculation and Consensus Using Linear Iterative Strategies
, 2007
"... Given an arbitrary network of interconnected nodes, we develop and analyze a distributed strategy that enables a subset of the nodes to calculate any given function of the node values. Our scheme utilizes a linear iteration where, at each timestep, each node updates its value to be a weighted avera ..."
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Cited by 47 (12 self)
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Given an arbitrary network of interconnected nodes, we develop and analyze a distributed strategy that enables a subset of the nodes to calculate any given function of the node values. Our scheme utilizes a linear iteration where, at each timestep, each node updates its value to be a weighted average of its own previous value and those of its neighbors. We show that this approach can be viewed as a linear dynamical system, with dynamics that are given by the weight matrix of the linear iteration, and with outputs for each node that are captured by the set of values that are available to that node at each timestep. In networks with timeinvariant topologies, we use observability theory to show that after running the linear iteration for a finite number of timesteps with almost any choice of weight matrix, each node obtains enough information to calculate any arbitrary function of the initial node values. The problem of distributed consensus via linear iterations, where all nodes in the network calculate the same function, is treated as a special case of our approach. In particular, our scheme allows nodes in networks with timeinvariant topologies to reach consensus on any arbitrary function of the initial node values in a finite number of steps for almost any choice of weight matrix.
Asynchronous consensus in continuoustime multiagent systems with switching topology and timevarying delays
 IEEE Transactions on Automatic Control
, 2008
"... In this paper, we study asynchronous consensus problems of continuoustime multiagent systems with discontinuous information transmission. The proposed consensus control strategy is implemented only based on the state information at some discrete times of each agent’s neighbors. The asynchronization ..."
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Cited by 46 (1 self)
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In this paper, we study asynchronous consensus problems of continuoustime multiagent systems with discontinuous information transmission. The proposed consensus control strategy is implemented only based on the state information at some discrete times of each agent’s neighbors. The asynchronization means that each agent’s update times, at which the agent adjusts its dynamics, are independent of others’. Furthermore, it is assumed that the communication topology among agents is timedependent and the information transmission is with bounded timevarying delays. If the union of the communication topology across any time interval with some given length contains a spanning tree, the consensus problem is shown to be solvable. The analysis tool developed in this paper is based on the nonnegative matrix theory and graph theory. The main contribution of this paper is to provide a valid distributed consensus algorithm that overcomes the difficulties caused by unreliable communication channels, such as intermittent information transmission, switching communication topology, and timevarying communication delays, and therefore has its obvious practical applications. Simulation examples are provided to demonstrate the effectiveness of our theoretical results. Key words: Multiagent systems, asynchronous consensus, switching topology, timevarying delays, coordination. PACS:
Sensor networks with random links: Topology design for distributed consensus
 IEEE Trans. on Signal Processing, http://arxiv.org/PS cache/arxiv/pdf/0704/0704.0954v1.pdf
, 2007
"... In a sensor network, in practice, the communication among sensors is subject to: (1) errors or failures at random times; (2) costs; and (3) constraints since sensors and networks operate under scarce resources, such as power, data rate, or communication. The signaltonoise ratio (SNR) is usually a ..."
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Cited by 38 (15 self)
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In a sensor network, in practice, the communication among sensors is subject to: (1) errors or failures at random times; (2) costs; and (3) constraints since sensors and networks operate under scarce resources, such as power, data rate, or communication. The signaltonoise ratio (SNR) is usually a main factor in determining the probability of error (or of communication failure) in a link. These probabilities are then a proxy for the SNR under which the links operate. The paper studies the problem of designing the topology, i.e., assigning the probabilities of reliable communication among sensors (or of link failures) to maximize the rate of convergence of average consensus, when the link communication costs are taken into account, and there is an overall communication budget constraint. To consider this problem, we address a number of preliminary issues: (1) model the network as a random topology; (2) establish necessary and sufficient conditions for mean square sense (mss) and almost sure (a.s.) convergence of average consensus when network links fail; and, in particular, (3) show that a necessary and sufficient condition for both mss and a.s. convergence is for the algebraic connectivity of the mean graph describing the network topology to be strictly positive. With these results, we formulate topology design, subject to random link failures and to a communication cost constraint, as a constrained convex optimization problem to which we apply semidefinite programming techniques. We show by an extensive numerical study that the optimal design improves significantly the convergence speed of the consensus algorithm and can achieve the asymptotic performance of a nonrandom network at a fraction of the communication cost.
Finitetime consensus problems for networks of dynamic agents
 IEEE Transactions on Automatic Control
, 2010
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Distributed consensus with limited communication data rate
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 2011
"... Communication data rate and energy constraints are important factors which have to be considered when investigating distributed coordination of multiagent networks. Although many proposed averageconsensus protocols are available, a fundamental theoretic problem remains open, namely, how many bits ..."
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Cited by 27 (3 self)
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Communication data rate and energy constraints are important factors which have to be considered when investigating distributed coordination of multiagent networks. Although many proposed averageconsensus protocols are available, a fundamental theoretic problem remains open, namely, how many bits of information are necessary for each pair of adjacent agents to exchange at each time step to ensure average consensus? In this paper, we consider averageconsensus control of undirected networks of discretetime firstorder agents under communication constraints. Each agent has a realvalued state but can only exchange symbolic data with its neighbors. A distributed protocol is proposed based on dynamic encoding and decoding. It is proved that under the protocol designed, for a connected network, average consensus can be achieved with an exponential convergence rate based on merely one bit information exchange between each pair of adjacent agents at each time step. An explicit form of the asymptotic convergence rate is given. It is shown that as the number of agents increases, the asymptotic convergence rate is related to the scale of the network, the number of quantization levels and the ratio of the second smallest eigenvalue to the largest eigenvalue of the Laplacian of the communication graph. We also give a performance index to characterize the total communication energy to achieve average consensus and show that the minimization of the communication energy leads to a tradeoff between the convergence rate and the number of quantization levels.
A distributed consensusbased cooperative spectrumsensing scheme in cognitive radios
 IEEE Transactions on Vehicular Technology
, 2010
"... Abstract—In cognitive radio (CR) networks, secondary users can cooperatively sense the spectrum to detect the presence of primary users. In this paper, we propose a fully distributed and scalable cooperative spectrumsensing scheme based on recent advances in consensus algorithms. In the proposed sc ..."
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Cited by 27 (5 self)
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Abstract—In cognitive radio (CR) networks, secondary users can cooperatively sense the spectrum to detect the presence of primary users. In this paper, we propose a fully distributed and scalable cooperative spectrumsensing scheme based on recent advances in consensus algorithms. In the proposed scheme, the secondary users can maintain coordination based on only local information exchange without a centralized common receiver. Unlike most of the existing decision rules, such as the ORrule or the 1outofN rule, we use the consensus of secondary users to make the final decision. Simulation results show that the proposed consensus scheme can have significant lower missing detection probabilities and false alarm probabilities in CR networks. It is also demonstrated that the proposed scheme not only has proven sensitivity in detecting the primary user’s presence but also has robustness in choosing a desirable decision threshold. Index Terms—Cognitive radios (CRs), consensus, cooperative spectrum sensing, random graphs. I.