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Adaptive Third-Order Leader-Following Consensus of Nonlinear Multi-agent Systems with Perturbations

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Chinese Physics Letters 2012年第2期29卷 37-40页

作者： SUN Mei CHEN Ying CAO Long WANG Xiao-Fang Nonlinear Scientific Research Center Jiangsu UniversityZhenjiang 212013

We investigate the third-order leader-following consensus problem of nonlinear multi-agent systems in undirected network *** on graph theory and Lyapunov stability theory,the adaptive control method is employed to achieve leader-following consensus in an undirected network of agents with nonlinear third-order dynamics against the *** examples validate the correctness of the results and show that the control gains have a great influence on the convergence performance of errors for a short time.

关键词： undirected nonlinear Nonlinear

Search for Directed Networks by Different Random Walk Strategies

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Chinese Physics Letters 2012年第3期29卷 263-266页

作者： ZHU Zi-Qi JIN Xiao-Ling HUANG Zhi-Long Department of Engineering Mechanics Zhejiang UniversityHangzhou 310027

A comparative study is carried out on the effciency of five different random walk strategies searching on directed networks constructed based on several typical complex *** to the difference in search effciency of the strategies rooted in network clustering,the clustering coeFfcient in a random walker's eye on directed networks is defined and computed to be half of the corresponding undirected *** search processes are performed on the directed networks based on Erd(o)s-Rényi model,Watts-Strogatz model,Barabási-Albert model and clustered scale-free network *** is found that self-avoiding random walk strategy is the best search strategy for such directed *** to unrestricted random walk strategy,path-iteration-avoiding random walks can also make the search process much more ***,no-triangle-loop and no-quadrangle-loop random walks do not improve the search effciency as expected,which is different from those on undirected networks since the clustering coefficient of directed networks are smaller than that of undirected networks.

关键词： undirected directed random

SDGNN: Symmetry-Preserving Dual-Stream Graph Neural Networks

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IEEE/CAA Journal of Automatica Sinica 2024年第7期11卷 1717-1719页

作者： Jiufang Chen Ye Yuan Xin Luo the College of Computer Science and Technology Chongqing University of Posts and TelecommunicationsChongqing 400065 the Chongqing Key Laboratory of Big Data and Intelligent Computing Chongqing Institute of Green and Intelligent TechnologyChinese Academy of SciencesChongqing 400714China the College of Computer and Information Science Southwest UniversityChongqing 400715China IEEE

Dear Editor,This letter proposes a symmetry-preserving dual-stream graph neural network(SDGNN) for precise representation learning to an undirected weighted graph(UWG). Although existing graph neural networks(GNNs) are influential instruments for representation learning to a UWG, they invariably adopt a unique node feature matrix for illustrating the sole node set of a UWG.

关键词： representation preserving undirected

Enhancing Controllability Robustness of q-Snapback Networks through Redirecting Edges

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Research 2019年第1期2019卷 719-741页

作者： Yang Lou Lin Wang Guanrong Chen City University of Hong Kong Hong Kong Shanghai Jiao Tong University Shanghai 200240China

Te well-known small-world network model was established by randomly rewiring edges,aiming to enhance the synchronizability of an undirected nearest-neighbor regular *** paper demonstrates via extensive numerical simulations that randomly redirecting edges could enhance the robustness of the network controllability for directed snapback networks against both random and intentional node-removal and edge-removal attacks.

关键词： undirected directed neighbor

EDGE-DISJOINT HAMILTONIAN CYCLES IN GRAPHS

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Chinese Science Bulletin 1991年第12期36卷 1055-1056页

作者：李明楚刘振宏 Department of Mathematics Beijing University of Science and Technology Beijing 100083 PRC Institute of Systems Science Academia Sinica Beijing 100080 PRC

All graphs considered here are undirected and finite, without loops or multiple edges. Let δ(G)denote the minimum degree of a graph G. A graph G is called Ore-type-(k)(where k is an integer) if d(u)+d(v)≥|V(G)|+k fo... 详细信息

关键词： undirected integer vertex conjecture

NEW SUFFICIENT CONDITIONS OF THE LONGEST CYCLES OF 1-TOUGH GRAPHS

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Chinese Science Bulletin 1991年第3期36卷 261-262页

作者：田永成 Department of Mathematics Northeast Institute of Technology Shengyang 110006 PRC

In this letter all graphs will be finite, undirected simple graphs. Let G be a graph. We shall use V(G), E and c(G) to denote the vertex set, the edge set and the circumference of G respectively. We denote the distanc... 详细信息

关键词： undirected vertex letter connected circumference 孟玉孟之公之

On (g, f)-Uniform Graphs

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数学进展 2000年第3期29卷 285-287页

作者：刘桂真 Dept.of Math. Shandong Univ.Jinan

　　The graphs considered in this paper will be simple undirected graphs. Let G be a graph with vertex set V(G) and edge set E(G). For a vertex x of G, the degree of x in G is denoted by Dg(x).

关键词： (g,f)-Uniform graphs simple undirected graph

Push-Pull Finite-Time Convergence Distributed Optimization Algorithm

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American Journal of Computational Mathematics 2020年第1期10卷 118-146页

作者： Xiaobiao Chen Kaixin Yan Yu Gao Xuefeng Xu Kang Yan Jing Wang Department of Science Taiyuan University of Technology Taiyuan China Department of Automation Taiyuan University of Technology Taiyuan China Department of Automation School of Control and Computer Engineering North China Electric Power University Beijing China Department of Economics and Management Taiyuan University of Technology Taiyuan China Department of Mechanical and Electrical Engineering Shanxi Energy Institute Taiyuan China School of Medicine Clinical Medicine Datong University Datong China

With the widespread application of distributed systems, many problems need to be solved urgently. How to design distributed optimization strategies has become a research hotspot. This article focuses on the solution rate of the distributed convex optimization algorithm. Each agent in the network has its own convex cost function. We consider a gradient-based distributed method and use a push-pull gradient algorithm to minimize the total cost function. Inspired by the current multi-agent consensus cooperation protocol for distributed convex optimization algorithm, a distributed convex optimization algorithm with finite time convergence is proposed and studied. In the end, based on a fixed undirected distributed network topology, a fast convergent distributed cooperative learning method based on a linear parameterized neural network is proposed, which is different from the existing distributed convex optimization algorithms that can achieve exponential convergence. The algorithm can achieve finite-time convergence. The convergence of the algorithm can be guaranteed by the Lyapunov method. The corresponding simulation examples also show the effectiveness of the algorithm intuitively. Compared with other algorithms, this algorithm is competitive.

关键词： Distributed Optimization Finite Time Convergence Linear Parameterized Neural Network Push-Pull Algorithm undirected Graph

Improved Approximation of Layout Problems on Random Graphs

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Open Journal of Discrete Mathematics 2020年第1期10卷 13-30页

作者： Kevin K. H. Cheung Patrick Girardet School of Mathematics and Statistics Carleton University Ottawa ON Canada Department of Mathematics University of California San Diego La Jolla CA USA

Inspired by previous work of Diaz, Petit, Serna, and Trevisan (Approximating layout problems on random graphs, Discrete Mathematics, 235, 2001, 245-253), we show that several well-known graph layout problems are approximable to within a factor arbitrarily close to 1 of the optimal with high probability for random graphs drawn from an Erdös-Renyi distribution with appropriate sparsity conditions using only elementary probabilistic analysis. Moreover, we show that the same results hold for the analogous problems on directed acyclic graphs.

关键词： Graph Arrangements Random Graphs Approximation Algorithms undirected Graphs Directed Acyclic Graphs