Distributed optimisation and control of graph Laplacian eigenvalues for robust consensus via an adaptive multilayer strategy

Kempton, Louis; Herrmann, Guido; Bernardo, Mario di

doi:10.1002/rnc.3808

Cited by 15 publications

(11 citation statements)

References 39 publications

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“…On the other hand, the largest Laplacian eigenvalue is an important factor to decide the stability of the system. For example, minimizing the spectral radius in [9] leads to maximize the robustness of the network to time delays under a linear consensus protocol. Furthermore, to speed up consensus algorithms, the optimal Laplacian-based consensus matrix is obtained with a stepsize which is the inverse of the sum of the smallest and the largest non-zero graph Laplacian eigenvalue [10].…”

Section: Introductionmentioning

confidence: 99%

Concensus-Based ALADIN Method to Faster the Decentralized Estimation of Laplacian Spectrum

Tran

Doan

2020

Applied Sciences

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With the upcoming fifth Industrial Revolution, humans and collaborative robots will dance together in production. They themselves act as an agent in a connected world, understood as a multi-agent system, in which the Laplacian spectrum plays an important role since it can define the connection of the complex networks as well as depict the robustness. In addition, the Laplacian spectrum can locally check the controllability and observability of a dynamic controlled network, etc. This paper presents a new method, which is based on the Augmented Lagrange based Alternating Direction Inexact Newton (ALADIN) method, to faster the convergence rate of the Laplacian Spectrum Estimation via factorization of the average consensus matrices, that are expressed as Laplacian-based matrices problems. Herein, the non-zero distinct Laplacian eigenvalues are the inverse of the stepsizes {αt,t=1,2,…} of those matrices. Therefore, the problem now is to carry out the agreement on the stepsize values for all agents in the given network while ensuring the factorization of average consensus matrices to be accomplished. Furthermore, in order to obtain the entire Laplacian spectrum, it is necessary to estimate the relevant multiplicities of these distinct eigenvalues. Consequently, a non-convex optimization problem is formed and solved using ALADIN method. The effectiveness of the proposed method is evaluated through the simulation results and the comparison with the Lagrange-based method in advance.

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Section: Introductionmentioning

confidence: 99%

Concensus-Based ALADIN Method to Faster the Decentralized Estimation of Laplacian Spectrum

Tran

Doan

2020

Applied Sciences

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“…Over the past few decades, considerable attention has been brought to the consensus of the multiagent systems because of its scientific significance and widespread application in satellite coordination control, mobile robot formation control, network congestion control, etc . The consensus of multiagent systems depend on internal dynamics, communication topology, and other factors; many researchers have made unremitting efforts in these directions …”

Section: Introductionmentioning

confidence: 99%

“…[1][2][3][4][5] The consensus of multiagent systems depend on internal dynamics, communication topology, and other factors; many researchers have made unremitting efforts in these directions. [6][7][8][9][10] The internal dynamics of multiagent systems play a crucial role in the consensus analysis. The early research about the consensus was mainly conducted under the framework of linear systems.…”

Section: Introductionmentioning

confidence: 99%

Consensus of multiagent systems with nonlinear dynamics and time‐varying communication delays

Qian

Gao

Wang

et al. 2019

Intl J Robust & Nonlinear

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Summary This paper deals with the local consensus of multiagent systems with nonlinear dynamics communication delays simultaneously. By introducing a weighted average state and applying the properties of the Laplacian matrix eigenvalues, the system is decoupled into several subsystems, firstly, to reduce complexity of theory analysis. Then, a new augmented vector containing single and double integral terms is constructed and the corresponding Lyapunov functional with triple integral terms is introduced. Meanwhile, in order to improve the estimating accuracy of the derivatives of constructed Lyapunov functional, single integral inequalities and double integral inequalities via auxiliary functions, an extended relaxed integral inequality and an reciprocally convex approach are used, as a result, stability criterion with less conservatism is derived, which guarantees the local consensus of the considered systems. Finally, numerical examples are provided to check the improvement of the proposed method over the existing works.

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“…Kempton et al . propose a distributed‐control approach to maximize the robustness of the network to time delays in linear‐consensus protocol. The method uses a multi‐layer distributed estimation strategy to solve the constrained optimization problem.…”

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confidence: 99%

Guest editorial: special issue on Consensus‐based Applications in Networked Systems

Chen

et al. 2017

Intl J Robust & Nonlinear

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Consensus, as an efficient distributed computing method, has been studied for several decades. The researchers within this area mainly focus on theoretical analysis of general consensus algorithm for different scenarios, for example, stability analysis under dynamic topologies and time delays, asynchronous and quantized consensus, and performance evaluation including convergence speed, accuracy, robustness, etc. However, existing works have rarely considered consensus in practical application scenarios, especially for the newly emerging distributed networked systems such as wireless sensor networks, cyber physical systems and smart grids, where there exist rich research opportunities in both theoretical and practical aspects. The objective of this special issue is to link the practical challenges and requirements with the theoretical advances in consensus. This special issue contains 17 papers that represent the state of the art in the research area of the consensus and its applications in networked systems. The papers address a variety of applications and cover a breadth of topics, ranging from theory to high-performance algorithms.Lu and Liu [1] focus on theoretical analysis of consensus, where the consensus problem for linear multi-agent systems subject to non-uniform time-varying communication delays and jointly connected switching networks is investigated. Both state feedback law and output feedback law are proposed to handle the consensus problem.Wu and Wang [2] investigate the problem of the mixed H2/H∞ synchronization control for the coupled partial differential systems. The sufficient conditions guaranteeing the existence of the solution are provided.Lei et al.[3] investigate security issues of consensus-based distributed estimation problem, considering the false data-injection attack. An optimal estimator is designed by minimizing the estimation error of each sensor under hostile attackers, and a set of suboptimal attacking sequence is provided. Nguyen and Dankowicz [4] investigate the synchronization and consensus problem of networked manipulators working on an underactuated-dynamic platform with communication delays. A leader-follower consensus scheme is proposed to track the constant and time-varying reference values. The tracking synchronization objective is achieved despite the effects of the communication delay and the unknown dynamics of the platform.Liu et al.[5] describe a dynamic coupling structure for the cluster synchronization problem with coupled-nonidentical linear systems. Lyapunov stability analysis method is used to obtain algebraic and graph topological conditions for cluster synchronization.Ou et al.[6] introduce methods for decentralized minimal-time formation control problems, including static and dynamic cases, respectively. The decentralized minimal-time static-formation method utilizes minimal polynomial to compute the final formation positions, and a Kroneckertheorem-based algorithm is proposed for the dynamic cases. Kempton et al. [7] propose a distributed-control approach ...

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Distributed optimisation and control of graph Laplacian eigenvalues for robust consensus via an adaptive multilayer strategy

Cited by 15 publications

References 39 publications

Concensus-Based ALADIN Method to Faster the Decentralized Estimation of Laplacian Spectrum

Concensus-Based ALADIN Method to Faster the Decentralized Estimation of Laplacian Spectrum

Consensus of multiagent systems with nonlinear dynamics and time‐varying communication delays

Guest editorial: special issue on Consensus‐based Applications in Networked Systems

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