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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 82 (20 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 62 (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.
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 (16 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.
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 38 (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:
Finitetime consensus problems for networks of dynamic agents
 IEEE Transactions on Automatic Control
, 2010
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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 26 (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.
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 26 (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.
Stochastic approximation for consensus seeking: mean square and almost sure convergence
 in Proceedings of the 46th IEEE Conference on Decision and Control
"... Abstract — We consider stochastic consensus problems in strongly connected directed graph models where each agent has noisy measurements of its neighbors ’ states. For consensus seeking, we develop stochastic approximation type algorithms with a decreasing step size and establish mean square and alm ..."
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Cited by 25 (1 self)
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Abstract — We consider stochastic consensus problems in strongly connected directed graph models where each agent has noisy measurements of its neighbors ’ states. For consensus seeking, we develop stochastic approximation type algorithms with a decreasing step size and establish mean square and almost sure convergence of the agents ’ states to the same limit. I.
Robustness of noisy consensus dynamics with directed communication
 in Proceedings of the American Control Conference
, 2010
"... Abstract — In this paper we study robustness of consensus in networks of coupled single integrators driven by white noise. Robustness is quantified as the H2 norm of the closedloop system. In particular we investigate how robustness depends on the properties of the underlying (directed) communicati ..."
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Cited by 25 (7 self)
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Abstract — In this paper we study robustness of consensus in networks of coupled single integrators driven by white noise. Robustness is quantified as the H2 norm of the closedloop system. In particular we investigate how robustness depends on the properties of the underlying (directed) communication graph. To this end several classes of directed and undirected communication topologies are analyzed and compared. The tradeoff between speed of convergence and robustness to noise is also investigated. I.
Agreement with NonUniform Information Delays
, 2006
"... We propose a novel agreement framework for multiple (possibly heterogeneous) agents evolving on a directed information graph with nonuniform delays. Our proposed framework can ensure agreement of a certain scalar quantity among the agents, as long as 1) for each agent, we can design a local contr ..."
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Cited by 23 (2 self)
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We propose a novel agreement framework for multiple (possibly heterogeneous) agents evolving on a directed information graph with nonuniform delays. Our proposed framework can ensure agreement of a certain scalar quantity among the agents, as long as 1) for each agent, we can design a local control s.t. its closedloop transfer function has unit gain at dc and gain strictly less than unity elsewhere; 2) the information graph has a globally reachable node (i.e. there exists a path from it to every other nodes); and 3) the information delays are finite constants. Rendezvous simulation is performed to verify the theory.