Ultrafast consensus in small-world networks

By Reza Olfati-Saber. Proceedings of the 2005, American Control Conference, 2005., 2005

418 citations recorded by the source corpus.

Subfields: Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/dc2894187aa9c0058efea2904020f59587b211a1

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In Condensed Matter Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Decentralised minimal-time consensus (2011, background): “Various applications can be cast in this framework, including swarming and ﬂocking [1], [2], distributed computing [3], agreement in social networks [4], [5] or synchronisation of coupled oscillators [6], [7], [8].”
Asynchronous Consensus Protocols Using Nonlinear Paracontractions Theory (2008, background): “For large or random networks, rewiring only a small portions of existing links would result in a fast consensus seeking [7].”
Distributed Kalman filtering based on consensus strategies (2008, background): “Many interes ting results have appeared recently [30][15][25][10] just to name a few.”
Multi-Agent Coordination by Decentralized Estimation and Control (2008, background): “The rate of convergence as a function of the network topology and weights, as well as heuristic and analytic approaches to choosing network topologies and weights to optimize convergence rates, are studied in [28], [31], [45], [46].”
Algebraic Connectivity of Interdependent Networks (2014, background): “This metric plays an important role on, among others, synchronization of coupled oscillators, network robustness, consensus problems, belief propagation, graph partitioning, and distributed filtering in sensor networks [14, 15, 16, 17, 18].”
Sensor Networks With Random Links: Topology Design for Distributed Consensus (2007, background): “References [7] and [8] consider restrict it to classes of random gr aphs, in particular, small-world topologies.”
Distributed finite-time tracking control for multi-agent systems: An observer-based approach (2013, methodology): “To obtain faster convergence rate, various consensus protocols with larger coupling strength, better communication topology and the optimal gain were designed and analyzed [11–15].”
Collective behavior coordination with predictive mechanisms (2008, methodology): “To improve the speed of convergence towards consensus for homogeneous networks, Olfati-Saber and Murray proposed a method based on the addition of a few long links to a regular lattice, thus transforming it into a small-world network [15], [16].”
Agreement over random networks (2004, background): “Small-world networks [21], [23], capturing some of the central features of social networks by exhibiting”
Consensus Filters for Sensor Networks and Distributed Sensor Fusion (2005, background): “Consensus problems [18], [21] for networked dynamic systems have been extensively used by many researchers as part of the solution of more complex problems including collective control of motion of swarms/flocks of mobile agents [15], ultrafast consensus in small-world networks [16], [24], state-dep”
Distributed Kalman Filter with Embedded Consensus Filters (2005, methodology): “A scheme for approximate distributed Kalman filtering (DKF) was proposed in [30] based on reaching an average-consensus [23], [27], [21].”
Delay robustness in consensus problems (2010, background): “Olfati-Saber (2005), conditions (19)–(21) are not independent of the topology but depend on the connectivity of the underlying graph.”
Flocking for multi-agent dynamic systems: algorithms and theory (2006, background): “[37] on coordination of mobile sensor networks; Khatib [38] and Rimon and Koditschek [39] on using artificial potentials for obstacle avoidance; Strogatz [40] on complex biological and social networks; and Olfati-Saber [41] on ultrafast small-world networks.”
Synchronization in complex networks (2008, methodology): “When applying this framework to a certain class of networks, Olfati-Saber (2005) finds that the speed of convergence, as the inverse of λ2 (as was also found in synchronization problems (Almendral and Dı́az-Guilera, 2007)), can be increased by orders of magnitude by simply rewiring a regular…”
Communication constraints in the average consensus problem (2008, background): “In [30] it is shown that some random rewiring can correct this slow convergence rate.”
Algebraic Connectivity Ratio of Ramanujan Graphs (2007, background): “Some problems in which algebraic connectivity plays a central role include consensus problems [22], [29], [24], [11], [26], [4], [20], [7], synchronization of coupled oscillators [27], flocking and swarming [19], [9], belief propagation and distributed hypothesis testing [21], and distributed filter”
Finite-Time Consensus Problems for Networks of Dynamic Agents (2007, background): “Simulation results showed that the interaction graph with small-world property possesses large algebraic connectivity [5].”