Bipartite consensus of multi-agent systems over signed graphs: State feedback and output feedback control approaches

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Summary This paper studies sign consensus, a collective behavior of multiagent systems, when both cooperative and antagonistic interactions coexist among agents. By sign consensus, it means that the states of all agents will eventually achieve the same sign but may with different magnitudes. Compared with some recent works on sign‐consensus problems, where only fixed graphs are considered and the graph adjacency matrix needs to be eventually positive, this paper allows the graph to be switching over time. Control laws are proposed and analyzed with respect to three classes of switching graphs. Examples illustrate the efficacy of the control algorithms.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sign‐consensus over cooperative‐antagonistic networks with switching topologies

Jiang

Zhang

Chen

2018

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“…Much progress has been made in the bipartite consensus of signed networked systems with first‐order agent dynamics: Hu and Zheng addressed the bipartite leaderless consensus of signed graphs containing a directed spanning tree; Xia et al analyzed the bipartite consensus in social networks with both trust and mistrust relationships; Meng et al introduced the concept of interval bipartite consensus for a signed network with structurally unbalanced topology. To extend the results of first‐order signed networks, some researchers considered the bipartite consensus of signed networks with more general agent dynamics: Hu and Zhu considered the bipartite leader‐following consensus of multiagent systems with second‐order dynamics; Valcher and Misra discussed the bipartite consensus of high‐order multiagent systems; Zhang and Chen studied the bipartite consensus problem for multiagent systems with general linear dynamics based on state‐ and output‐feedback control approaches. In recent years, other types of collective behaviors of signed networks have also been investigated: Fan et al considered the bipartite flocking of second‐order multiagent systems under signed graphs; Meng addressed the bipartite containment control of signed networks with multiple leaders.…”

Section: Introductionmentioning

confidence: 99%

Bipartite synchronization of Lur'e network under signed digraph

Liu

Song

Wen

et al. 2018

Summary This paper considers the bipartite leaderless and leader‐following synchronization in a network of coupled Lur'e systems with sector‐condition node dynamics and signed digraph topology, where the interaction digraph consists of both positive and negative communication links. Continuous‐time and sampled‐data control algorithms are, respectively, proposed to solve the bipartite synchronization problems for the signed Lur'e network. Under some assumptions on the network structure and node functions, some bipartite synchronization conditions are established for signed Lur'e network by using coordinate transform, linear matrix inequalities, and algebraic graph theories. For the continuous‐time control algorithms, it is shown that the bipartite synchronization problems of the signed Lur'e network can always be solved if the coupling strength is sufficiently large and the network topology satisfies some suitable conditions. For the sampled‐data control algorithms, an upper bound of the sampling intervals is estimated to ensure that the bipartite synchronization can be reached in the signed Lur'e network. Some simulation results are given to illustrate the effectiveness of the theoretical analysis.

“…Therefore, it is of practical importance to investigate the bipartite control problem over signed digraph. Collective behaviors of homogeneous MAS over signed digraph have been studied in the literature –. Altafini has developed the concept of bipartite consensus among agents with antagonistic interactions based on properties of signed weighted graphs and the associated Laplacian matrices.…”

Section: Introductionmentioning

confidence: 99%

Bipartite output synchronization of heterogeneous multiagent systems on signed digraphs

Zuo

Lewis²,

Song

et al. 2018

Summary This paper studies the bipartite output synchronization problem of general linear heterogeneous multiagent systems on signed digraphs. We first show that, for heterogeneous multiagent systems, the bipartite output synchronization over the structurally balanced signed digraphs and the conventional output synchronization over the associated nonnegative digraphs are equivalent. Then, 3 different control protocols, using full‐state feedback, static output feedback, and dynamic output feedback are designed at each agent to solve the bipartite output synchronization problem based on solutions to the corresponding output regulator equations. Explicit local design procedures are proposed for all 3 control protocols. The compensators employed in these protocols incorporate only one copy of the virtual exosystem's dynamics, regardless of the dimensions of the outputs. This results in lower‐dimensional compensators and controllers and, hence, is more computationally tractable compared to the popular internal model principle‐based control protocols. Numerical simulations over 3 different signed communication digraphs validate the proposed control protocols.