Convergence of Type-Symmetric and Cut-Balanced Consensus Seeking Systems

Hendrickx, Julien M.; Tsitsiklis, John N.

doi:10.1109/tac.2012.2203214

Cited by 184 publications

(255 citation statements)

References 30 publications

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“…Moreover, simple conditions for two agents to converge to the same value are then available. These results were established for continuoustime system in [8]. Related observations for discrete-time systems were made in [3], [11], [10], (see also references in [8]).…”

Section: Comparison With Existing Literaturementioning

confidence: 62%

“…where the coefficients α h,k are This lemma allows us to transform the network of secondorder dynamics in (10) into a network of first-order dynamics, and then to apply the convergence criteria in [8] on the resulting graphG. We are then ready to prove the main result of this paper.…”

Section: Assume That G ≥ 2d Imentioning

confidence: 96%

“…In doing so, it explores a new investigation line based on the cutbalance condition of [8]. The current manuscript still exhibits a few of the features of the approach in [6], which makes the contribution different from those in [18] and [7].…”

Section: Comparison With Existing Literaturementioning

confidence: 97%

“…Besides the extension to a more general class of multiagent systems, one of the main contributions of this work is the link that we establish between event-based coordination control and a recently proved sufficient condition for the convergence of consensus algorithms, involving very general cut-balance conditions [8]. Indeed, one of the difficulties that we face when going from first-order to second-order agents is that the Lyapunov-based analysis that was pursued in [6] can not be directly extended.…”

Section: Introductionmentioning

confidence: 99%

“…Indeed, one of the difficulties that we face when going from first-order to second-order agents is that the Lyapunov-based analysis that was pursued in [6] can not be directly extended. Instead of insisting on the search for an appropriate Lyapunov function (a topic that could nevertheless be of interest for future research), we pursue here a different approach relying on the results of [8].…”

Section: Introductionmentioning

confidence: 99%

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Self-triggered rendezvous of gossiping second-order agents

Persis

Frasca

Hendrickx

2013

52nd IEEE Conference on Decision and Control

Self Cite

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Abstract-A recent paper by some of the authors introduced several self-triggered coordination algorithms for first-order continuous-time systems. The extension of these algorithms to second-order agents is relevant in many practical applications but presents some challenges that are tackled in this contribution and that require to depart from the analysis that was carried out before. We design a self-triggered gossiping coordination algorithm that induces a time-varying communication graph, which is enough connected to guarantee useful convergence properties, and allows us to achieve the desired coordination task in a formation of double-integrator agents that (i) establish pair-wise communication at suitably designed times and (ii) exchange relative measurements while reducing the sensing and communication effort. , authors have been focusing on cooperative control problems in which the agents do not exchange information continuously but rather at times that are decided based on current local measurements. These coordination strategies can be of two types: event-triggered or self-triggered coordination control. The focus of this paper is on the second class of coordination control algorithms and is inspired by the socalled self-triggered gossiping algorithms of [6]. I. IntroductionThe term "self-triggered gossiping" refers to the way in which agents establish communication: each pair of agents connected by an edge of an undirected graph decide in realtime the next sampling time based on the local measurements. The design of these sampling times by a pair of connected nodes is performed in a completely independent way from the other pairs and results in an asynchronous information exchange pattern. Moreover, this approach can lead to a significant reduction of communication and sensor activity: at each sampling time the sensors of the connected agents switch to active mode, exchange measurements, compute the next sampling time and then go to sleep mode until the next sampling time is reached.

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Section: Comparison With Existing Literaturementioning

confidence: 62%

Section: Assume That G ≥ 2d Imentioning

confidence: 96%

Section: Comparison With Existing Literaturementioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Self-triggered rendezvous of gossiping second-order agents

Persis

Frasca

Hendrickx

2013

52nd IEEE Conference on Decision and Control

Self Cite

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Consensus in Multi‐Agent Systems

Proskurnikov

Cao

2016

Wiley Encyclopedia of Electrical and Electronics Engineering

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Many cooperative behaviors of multi‐agent teams emerge from local interactions among the agents, where an agent interacts with a few “adjacent” teammates, but has no information about the remaining agents. For instance, the self‐organization of many biological populations –including swarms of insects, flocks of birds, and schools of fish –are based on such local interaction rules: the motion and decisions of an individual agent are determined by the behavior of its nearest neighbors in the population. A special case of multi‐agent coordination is consensus , that is, the agreement of agents on some quantity of interest or, more generally, the full or partial synchronization of their state trajectories. Establishing consensus is a “benchmark” problem in multi‐agent systems study, which allows to reveal the main principles of multi‐agent coordination and, in particular, the role of the system's interaction graph (or topology). Consensus lies in the heart of many natural phenomena (e.g., synchronous oscillation of neural cells, which maintains a stable heart rhythm) and engineering designs (e.g., attitude synchronization of satellites). In this article, we give a brief review of distributed consensus algorithms, focusing on the basic ideas and relevant mathematical theory, in particular, graph‐theoretic methods.

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Consensus and influence power approximation in time‐varying and directed networks subject to perturbations

Martín

Morărescu

Nešić

2019

Intl J Robust & Nonlinear

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The paper focuses on the analysis of multi-agent systems interacting over directed and time-varying networks in presence of parametric uncertainty on the interaction weights. We assume that agents reach a consensus, and the main goal of this work is to characterize the contribution that each agent has to the consensus value. This information is important for network intervention applications such as targeted advertising over social networks. Indeed, for an advertising campaign to be efficient, it has to take into account the influence power of each agent in the graph (ie, the contribution of each agent to the final consensus value). In our first results, we analytically describe the trajectory of the overall network, and we provide lower and upper bounds on the corresponding consensus value. We show that under appropriate assumptions, the contribution of each agent to the consensus value is smooth both in time and in the variation of the uncertainty parameter. This allows approximating the contribution of each agent when small perturbations affect the influence of each agent on its neighbors. Finally, we provide a numerical example to illustrate how our theoretical results apply in the context of network intervention.

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Convergence of Type-Symmetric and Cut-Balanced Consensus Seeking Systems

Cited by 184 publications

References 30 publications

Self-triggered rendezvous of gossiping second-order agents

Self-triggered rendezvous of gossiping second-order agents

Consensus in Multi‐Agent Systems

Consensus and influence power approximation in time‐varying and directed networks subject to perturbations

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