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

Applied sciences, 2020-08, Vol.10 (16), p.5625 [Peer Reviewed Journal]

2020. This work is licensed under http://creativecommons.org/licenses/by/3.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. ;ISSN: 2076-3417 ;EISSN: 2076-3417 ;DOI: 10.3390/app10165625

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  • Title:
    Concensus-Based ALADIN Method to Faster the Decentralized Estimation of Laplacian Spectrum
  • Author: Tran, Thi-Minh-Dung ; Ngoc An, Luu ; Doan, Ngoc Chi Nam
  • Subjects: Alternating Direction of Multipliers Method (ADMM) ; augmented Lagrange based Alternating Direction Inexact Newton (ALADIN) method ; Connectivity ; consensus algorithms ; Control algorithms ; Controllability ; Convex analysis ; Dance ; Eigenvalues ; Factorization ; laplacian eigenvalues ; multi-agent systems ; Observability (systems) ; Optimization ; Stability
  • Is Part Of: Applied sciences, 2020-08, Vol.10 (16), p.5625
  • Description: 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.
  • Publisher: Basel: MDPI AG
  • Language: English
  • Identifier: ISSN: 2076-3417
    EISSN: 2076-3417
    DOI: 10.3390/app10165625
  • Source: ROAD: Directory of Open Access Scholarly Resources
    ProQuest Central
    DOAJ Directory of Open Access Journals
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