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Prescribed-time Bipartite Formation Tracking Control of Heterogeneous Networked Agent Systems Over signed graph

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Prescribed-time Bipartite Formation Tracking Control of Hete...

Yet More Elementary Proof of Matrix-Tree Theorem for signed graphs

第35届中国过程控制会议

作者： Haoyang Yuan Boxian Lin Shiji Tong Mengji Shi Kaiyu Qin Qiang Liu School of Aeronautics and Astronautics University of Electronic Science and Technology of China Aircraft Swarm Intelligent Sensing and Cooperative Control Key Laboratory of Sichuan Province National Laboratory on Adaptive Optics

This paper addresses the bipartite formation tracking control problem of heterogeneous networked agent *** interactions among agents are described by a signed graph,where cooperation and competition coexist. Theoretically, a prescribed-time control scheme is designed for follower agents to achieve bipartite formation tracking. At first, the output regulation equation is employed to establish a mapping between state and output. Subsequently, we model the issue as an error stabilization problem, which facilitates the design of the controller. Secondly, by generating the time-scaling function, a prescribed-time formation tracking controller is designed. Then,the stability of the closed-loop system is proven by utilizing the Lyapunov theorem. Finally, the effectiveness of the proposed prescribed-time bipartite formation tracking controller is verified by some simulation results.

关键词： Bipartite formation Prescribed-time Heterogeneous networked agent systems signed graph

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Algebra Colloquium 2023年第3期30卷 493-502页

作者： Shu Li Jianfeng Wang School of Mathematics and Statistics Shandong University of TechnologyZiboShandong 255049China

A signed graph G˙=(G,σ)is a graph G=(V(G),E(G))with vertex set V(G)and edge set E(G),together with a functionσ:E→{+1,−1}assigning a positive or negative sign to each *** this paper,we present a more elementary proof for the matrix-tree theorem of signed graphs,which is based on the relations between the incidence matrices and the Laplcians of signed *** an application,we also obtain the results of Monfared and Mallik about the matrix-tree theorem of graphs for signless Laplacians.

关键词： signed graph matrix-tree theorem Laplacian signless Laplacian incidence matrix

A Characterization of Bicyclic signed graphs with Nullity n-7

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Journal of Mathematical Research with Applications 2015年第1期35卷 1-10页

作者： Guojun LI Aimei YU Department of Mathematics Beijing Jiaotong University

Let Γ be a signed graph and A(Γ) be the adjacency matrix of Γ. The nullity ofΓ is the multiplicity of eigenvalue zero in the spectrum of A(Γ). In this paper, the connected bicyclic signed graphs(including simple ... 详细信息

关键词： nullity signed graph bicyclic graph adjacency matrix

Balanced Subeulerian signed graphs and signed Line graphs

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Journal of Mathematical Research with Applications 2024年第1期44卷 7-17页

作者： Juan LIU Hong YANG Xindong ZHANG Hongjian LAI College of Big Data Statistics Guizhou University of Finance and Economics College of Mathematics and System Sciences Xinjiang University Department of Mathematics West Virginia University

A signed graph S =(Su, σ) has an underlying graph Suand a function σ : E(Su)-→{+,-}. Let E-(S) denote the set of negative edges of S. Then S is eulerian signed graph(or subeulerian signed graph, or balanced eulerian signed graph, respectively) if Suis eulerian(or subeulerian, or eulerian and |E-(S)| is even, respectively). We say that S is balanced subeulerian signed graph if there exists a balanced eulerian signed graph S′ such that S′ is spanned by *** signed line graph L(S) of a signed graph S is a signed graph with the vertices of L(S) being the edges of S, where an edge eiej is in L(S) if and only if the edges ei and ej of S have a vertex in common in S such that an edge eiej in L(S) is negative if and only if both edges ei and ej are negative in S. In this paper, two families of signed graphs S and S ′ are identified, which are applied to characterize balanced subeulerian signed graphs and balanced subeulerian signed line graphs. In particular, it is proved that a signed graph S is balanced subeulerian if and only if S?S, and that a signed line graph of signed graph S is balanced subeulerian if and only if S?S ′.

关键词： signed graph signed line graph balanced eulerian balanced subeulerian

Nowhere-zero 15-Flow in 3-Edge-connected Bidirected graphs

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Acta Mathematica Sinica,English Series 2014年第4期30卷 649-660页

作者： Er Ling WEI Wen Liang TANG Dong YE Department of Mathematics Renmin University of China Department of Mathematics West Virginia University Department of Mathematical Sciences Middle Tennessee State University

It was conjectured by Bouchet that every bidirected graph which admits a nowhere-zero κ flow will admit a nowhere-zero 6-flow. He proved that the conjecture is true when 6 is replaced by 216. Zyka improved the result with 6 replaced by 30. Xu and Zhang showed that the conjecture is true for 6-edge-connected graphs. And for 4-edge-connected graphs, Raspaud and Zhu proved it is true with 6 replaced by 4. In this paper, we show that Bouchet＇s conjecture is true with 6 replaced by 15 for 3-edge-connected graphs.

关键词： Bidirected graph integer flow signed graph

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signed Zero-Divisor graphs Over Commutative Rings

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Communications in Mathematics and Statistics 2024年第3期12卷 463-477页

作者： Lu Lu Lihua Feng Weijun Liu School of Mathematics and Statistics HNP-LAMACentral South UniversityChangsha 410083HunanPeople’s Republic of China

In this paper,we define signed zero-divisor graphs over commutative rings and investigate the interplay between the algebraic properties of the rings and the combinatorial properties of their corresponding signed zero-divisor *** investigate the structure of signed zero-divisor graphs,the relation between ideals and signed zero-divisor graphs,and the adjacency matrices and the spectra of signed zero-divisor graphs.

关键词： Ring Ideal signed graph Adjacency matrix

Synchronization of second-order Kuramoto networks from the perspective of edge dynamics

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Control Theory and Technology 2023年第4期21卷 580-590页

作者： Liang Wu Jiuming Zhong Haoyong Chen School of Physics and Electronic Engineering Hainan Normal UniversityHaikou571158HainanChina School of Electric Power South China University of TechnologyGuangzhou510640GuangdongChina

This paper presents new synchronization conditions for second-order phase-coupled Kuramoto oscillators in terms of edge *** types of network-underlying graphs are studied,the positively weighted and signed graphs,*** apply an edge Laplacian matrix for a positively weighted network to represent the edge *** properties of the edge Laplacian matrix are analyzed and incorporated into the proposed *** conditions take account of the dynamics of edge-connected oscillators instead of all oscillator pairs in conventional *** a network with positive and negative weights,we represent the network by its spanning tree dynamics,and derive conditions to evaluate the synchronization state of this *** conditions show that if all edge weights in the spanning tree are positive,and the tree-induced dynamics are in a dominant position over the negative edge dynamics,then this network achieves *** theoretical findings are validated by numerical examples.

关键词： Kuramoto oscillator signed graph Synchronization Edge Laplacian matrix Spanning tree

Output Bipartite Consensus of Heterogeneous Linear Multi-Agent Systems Under Switching Topologies 36

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Output Bipartite Consensus of Heterogeneous Linear Multi-Age...

Neural Modified Extended State Observer for Autonomous Maritime Transportation Vehicles with Actuator Faults and Unmatched Nonlinearities

第36届中国控制会议

作者： Yueming Wang Meiling Cheng Hongwei Zhang School of Electrical Engineering Southwest Jiaotong University

ISBN: (纸本)9781538629185

This paper considers bipartite consensus of linear multi-agent systems over signed directed graphs,where both collaboration and competition *** agent dynamics are distinct and can all have different *** communication graph can be time-varying and need not to be connected at each time.A distributed control law is proposed which enables the group to split into two disjoint subgroups,and the outputs of all agents within each subgroup achieve consensus,but the two subgroups move oppositely towards each *** analysis and a simulation example are provided.

关键词： Heterogeneous linear multi-agent system Output bipartite consensus signed graph Switching topology

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Guidance, Navigation and Control 2024年第1期4卷 41-61页

作者： Yutao Wu Zehui Mao Bin Jiang College of Automation Engineering Nanjing University of Aeronautics and Astronautics Nanjing 210016 P.R.China

This paper investigates extended state observer design problem for autonomous maritime transportation vehicles consisting of multiple unmanned aerial vehicles(UAVs)and unmanned surface vehicles(USVs)via the cooperation–competition *** two coordinate transformations,the dynamic model of UAVs and USVs is transformed into a standard secondorder heterogeneous multi-agent system in unified earth-fixed *** order to recover the unavailable velocities,unpredictable fault,total disturbance as well as to estimate the heterogeneous match/unmatched nonlinearities,neural network(NN)is incorporated into the design process of the modified distributed extended state observer(MESO).Based on the Lyapunov stability analysis,it is proved that all the error signals are uniformly ultimately bounded(UUB)and the bounds could be arbitrarily small by choosing appropriate *** results verify the effectiveness of the proposed method.

关键词： UAVs-USVs neural network extended state observer signed graph

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