Convergence Time of Quantized Metropolis Consensus Over Time-Varying Networks

Başar, Tamer; Etesami, S. Rasoul; Olshevsky, Alex

doi:10.1109/tac.2016.2539547

Cited by 18 publications

(13 citation statements)

References 16 publications

(39 reference statements)

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“…. Therefore, BCD method applied to (8) In what follows next, we use the above Lyapunov function to establish asymptotic convergence of the restricted HK model to an equilibrium point in the absence of edge heterogeneity (i.e., when all ij are the same which by rescaling from now we may assume ij = 1, ∀i, j). To lower bound the decrease of Lyapunov function V (·) at a given time step t, we note that this decrease is lower bounded by the decrease amount which is achieved due to the state update.…”

Section: B Restricted Edge Heterogeneous Hk Dynamicsmentioning

confidence: 99%

A Simple Framework for Stability Analysis of State-Dependent Networks of Heterogeneous Agents

Etesami¹

2019

SIAM J. Control Optim.

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Stability and analysis of multi-agent network systems with state-dependent switching typologies have been a fundamental and longstanding challenge in control, social sciences, and many other related fields. These already complex systems become further complicated once one accounts for asymmetry or heterogeneity of the underlying agents/dynamics. Despite extensive progress in analysis of conventional networked decision systems where the network evolution and state dynamics are driven by independent or weakly coupled processes, most of the existing results fail to address multi-agent systems where the network and state dynamics are highly coupled and evolve based on status of heterogeneous agents. Motivated by numerous applications of such dynamics in social sciences, in this paper we provide a new direction toward analysis of dynamic networks of heterogeneous agents under complex time-varying environments. As a result we show how Lyapunov stability and convergence of several challenging problems from opinion dynamics can be established using a simple application of our framework. Moreover, we introduce a new class of asymmetric opinion dynamics, namely nearest neighbor dynamics, and show how our approach can be used to analyze their behavior. In particular, we extend our results to game-theoretic settings and provide new insights toward analysis of complex networked multi-agent systems using exciting field of sequential optimization.This function can also be written in a compact form as f (y, λ) = y T Ly − tr(L) 2 , where L := diag(λ1) − λ, and tr(·) denotes the trace function. Intuitively, the block variable λ is meant to capture the communication network G t , and the block variable y captures the opinion states. Note that if we restrict λ ij s to binary variables in {0, 1}, then λ simply represents the adjacency matrix of a network of n agents where λ ij = 1 if there is a directed edge (i, j) from node i to node j, and λ ij = 0 otherwise. Moreover, for such a binary block variable λ, the matrix L is precisely the Laplacian matrix of the communication network associated with λ. Although we still need to assume that λ ∈ {0, 1} n×n , to avoid complication of handling integral variables, for now we allow λ ij s to vary continuously in the interval [0, 1]. As we shall see soon the integrality of network variables will be automatically achieved during iterations of the BCD method. Now let us consider the BCD method applied to the objective function (5) with block variables x and λ. For a generic time t, let us fix the state variable to y = x(t). Minimizing (5) with respect to the network variable λ ∈ Λ = [0, 1] n×n we obtain, λ t := arg min λ∈[0,1] n 2 i,j

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Section: B Restricted Edge Heterogeneous Hk Dynamicsmentioning

confidence: 99%

A Simple Framework for Stability Analysis of State-Dependent Networks of Heterogeneous Agents

Etesami¹

2019

SIAM J. Control Optim.

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“…The factor of time-varying communication networks in DERC problem was discussed in [8][9][10]. A distributed approach with quadratic convergence rate was proved in [8] on condition of long-term connectivity undirected graphs.…”

Section: Introductionmentioning

confidence: 99%

Distributed accelerated descent algorithm for energy resource coordination in multi‐agent integrated energy systems

Kou

Wang

Bie

et al. 2021

IET Generation Trans & Dist

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Composed of multiple integrated energy systems (IESs) belonging to different stakeholders, multi-agent IESs (MA-IESs) are widely concerned because of data privacy protect. As the basis of planning design and reliability evaluation for MA-IESs, distributed energy resource coordination (DERC) problem is studied in this paper. First, a DERC model for MA-IESs is established, which considers energy conversion process specifically. Meanwhile, a novel distributed accelerated descent (DAD) algorithm is proposed to realize fully distributed solving. Different from most of the existing researches that investigate the DERC with box constraints, the presented algorithm is able to solve the DERC with general convex constraints. Moreover, the backward operators in the method improve the convergence rate to the best of distributed first-order optimization algorithm with fixed step size, O(1∕T). Furthermore, the presented approach is initialization robustness when the load fluctuations suddenly happened in MA-IESs. The convergence property, computing, and communication complexity are strictly proved. Finally, the effectiveness of DERC model and DAD algorithm are demonstrated by some modified case studies.

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“…The work of Başar et al . 29 defines the expected convergence rate of Quantized Metropolis consensus. The assumption though is that the graph remains connected in every sequence and that the transmission occurs to a single node per step with a uniform probability.…”

Section: Introductionmentioning

confidence: 99%

Timing Information Propagation in Interactive Networks

Hafnaoui

Nicolescu

Beltrame

2019

Sci Rep

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Animal behavior is greatly influenced by interaction between peers as well as with the environment. Understanding the flow of information between individuals can help decipher their behavior. This applies to both the microscopic and macroscopic levels, from cellular communication to coordinated actions by humans. The aim of this work is to provide a simple but sufficient model of information propagation to learn from natural coordinated behavior, and apply this knowledge to engineered systems. We develop a probabilistic model to infer the information propagation in a network of communicating agents with different degrees of interaction affinity. Another focus of the work is estimating the time needed to reach an agreement between all agents. We experiment using swarms of robots to emulate the communication of biological and social media groups for which we are able to provide upper bounds for the time needed to reach a global consensus, as well as to identify individuals that are responsible for slow convergence.

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Convergence Time of Quantized Metropolis Consensus Over Time-Varying Networks

Cited by 18 publications

References 16 publications

A Simple Framework for Stability Analysis of State-Dependent Networks of Heterogeneous Agents

A Simple Framework for Stability Analysis of State-Dependent Networks of Heterogeneous Agents

Distributed accelerated descent algorithm for energy resource coordination in multi‐agent integrated energy systems

Timing Information Propagation in Interactive Networks

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