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

Kempton L. C.; Herrmann G.; di?Bernardo M.

摘要

Summary xml:id="rnc3808-para-0001"> Functions of eigenvalues of the graph Laplacian matrix L , especially the extremal non‐trivial eigenvalues, the algebraic connectivity <fi>λ</fi> <sub>2</sub> and the spectral radius <fi>λ</fi> <sub> <fi>n</fi> </sub> , have been shown to be important in determining the performance in a host of consensus and synchronisation applications. In this paper, we focus on formulating an entirely distributed control law for the control of edge weights in an undirected graph to solve a constrained optimisation problem involving these extremal eigenvalues. xml:id="rnc3808-para-0002">As an objective for the distributed control law, edge weights must be found that minimise the spectral radius of the graph Laplacian, thereby maximising the robustness of the network to time delays under a simple linear consensus protocol. To constrain the problem, we use both local weight constraints that weights must be non‐negative, and a global connectivity constraint, maintaining a designated minimum algebraic connectivity. This ensures that the network remains sufficiently well connected. xml:id="rnc3808-para-0003"> The distributed control law is formulated as a multilayer strategy, using three layers of successive distributed estimation. Adequate timescale separation between the layers is of paramount importance for the proper functioning of the system, and we derive conditions under which the distributed system converges as we would expect for the centralised control or optimisation system to converge. ? 2017 The Authors International Journal of Robust and Nonlinear Control published by John Wiley & Sons Ltd. </abstract </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><abstract xmlns =“http://www.wiley.com/namespaces/wiley”type =“main”xml：id =“rnc3808-abs-0001”> <标题类型=“main”>摘要</ title> < P XML：ID =“RNC3808-段 - 0001”>图表的特征值的功能，图拉普拉斯矩阵 l </ b>，尤其是极值非琐蝇特征值，代数连通性<fi>λ</ fi> < Sub> 2 </ sub>和光谱半径<fi> <fi> <sub> <fi> n </ fi> </ sub>在确定在一系列共识中的性能方面是重要的和同步应用程序。在本文中，我们专注于制定一个完全分布的控制法，用于控制一个无向图中的边缘权重，以解决涉及这些极端特征值的受约束优化问题。作为分布式控制定律的目标，必须找到边缘权重，从而最大限度地减少图拉普拉斯的光谱半径，从而最大化网络的稳健性在简单的线性共识协议下的时间延迟。要限制问题，我们使用局部权重约束，重量必须是非负的，以及保持指定的最小代数连接的全局连接约束。这确保了网络保持得足够好。</ p> XML：ID =“RNC3808-PARA-0003”>分布式控制定律使用三层连续的分布式估计制定为多层策略。对于系统的适当运行，层之间的足够的时间尺度分离是至关重要的，并且我们推导了分布式系统收敛的条件，因为我们希望集中控制或优化系统收敛。还2017年的作者国际杂志Chinound and Nonlinear Control </ i>由John Wiley＆amp出版; SONS LTD. </ P> </摘要 </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-21736/'>《International Journal of Robust and Nonlinear Control》</a> <b style="margin: 0 2px;">|</b><span>2017年第9期</span><b style="margin: 0 2px;">|</b><span>共27页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Kempton L. C.&option=202" target="_blank" rel="nofollow">Kempton L. C.;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Herrmann G.&option=202" target="_blank" rel="nofollow">Herrmann G.;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=di?Bernardo M.&option=202" target="_blank" rel="nofollow">di?Bernardo M.;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Department of Engineering MathematicsUniversity of BristolBristol UK;</p> <p>Department of Mechanical EngineeringUniversity of BristolBristol UK;</p> <p>Department of Engineering MathematicsUniversity of BristolBristol UK;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/7742.html" title="自动化系统">自动化系统;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=distributed control and optimisation&option=203" rel="nofollow">distributed control and optimisation;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=robust consensus&option=203" rel="nofollow">robust consensus;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=multilayer networks&option=203" rel="nofollow">multilayer networks;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=singular perturbation theory&option=203" rel="nofollow">singular perturbation theory;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=graph Laplacian eigenvalues&option=203" rel="nofollow">graph Laplacian eigenvalues;</a> </p> <div class="translation"> 机译：分布式控制和优化;稳健的共识;多层网络;奇异扰动理论;图拉普拉斯特征值; </div> </li> </ul> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704023067219.html">Distributed optimisation and control of graph Laplacian eigenvalues for robust consensus via an adaptive multilayer strategy</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Kempton L. 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