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

Thi-Minh-Dung Tran,Ngoc Chi Nam Doan,Luu Ngoc An

doi:10.3390/app10165625

Thi-Minh-Dung Tran, Ngoc Chi Nam Doan + Show 1 more

Open Access

https://doi.org/10.3390/app10165625

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Abstract

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.

Highlights

Leaders around the world obviously prefer the present era of connectivity as the Fourth IndustrialRevolution [2]
We present an Augmented Lagrangian based Alternating Direction Inexact Newton (ALADIN) method to estimate the Laplacian spectrum in decentralized scheme for dynamic controlled networks
On the purpose of monitoring the connection of a large network G ∗ (V ∗, E∗ ), one may face with the numerical issue in step 3 of the ALADIN-based method to solve the linear system (19) due to the huge dimension of the obtained matrix that leads to the common ill-conditioning problem with the inverse matrix calculation

Summary

Introduction

Leaders around the world obviously prefer the present era of connectivity as the Fourth IndustrialRevolution [2]. Data and information from these different areas have been made available and have been connected in complex and dense networks. For better integration and utilization, control aspect of these complex networks, researchers from different communities have brought different contributions varying from topology inference to control strategy, deputizing for interacting systems, which are modeled by graphs, whose vertices represent the components of the system while edges stand for the interactions between these components. In the last decade there has been dramatic increasing number of publications in the cooperative control of multi-agent systems. In which interconnection is represented by G (V, E), an undirected graph with components’ set V and links’ set E, consisting of N = |V | nodes, let us denote by. Λ D+1 } stands for the set of the non-zero distinct Laplacian eigenvalues.

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