具有无界异构常时滞的连续时间多智能体系统的一致性能力：符号拉普拉斯视角
Consensusability of Continuous-Time Multi-Agent Systems With Unbounded Heterogeneous Constant Delays: A Signed Laplacian Perspective
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中文总结 AI 辅助
该研究结合频域分析与代数图论，构建符号拉普拉斯算子，推导时滞下连续时间多智能体系统的一致性条件，为时滞一致性机制提供新视角。
中文摘要 AI 辅助
结合频域分析与代数图论，研究具有无界异构常时滞的连续时间多智能体系统的一致性问题。构建了多种类型的符号拉普拉斯算子以表征时滞下的一致性能力，核心结果基于所定义的嵌入时滞的符号拉普拉斯算子建立：其中，小时滞链路会产生合作交互，而可能无界的大时滞链路则会在智能体间产生拮抗交互。小时滞与大时滞的分界线为τᵢⱼ=π/2λₘₐₓ(L₀)，其中λₘₐₓ(L₀)指常规图拉普拉斯算子的最大特征值。研究证明，若嵌入时滞的符号拉普拉斯算子为半正定且具有单零特征值，则一致性能力得以保持。此外，还基于扩展有效电阻推导了若干一致性条件，该电阻用于衡量两组智能体间的整体耦合关系。所得结果从底层网络拓扑中小时滞诱导的合作性与大时滞诱导的拮抗作用的相互作用角度，为时滞一致性的机制提供了新见解。
英文摘要
The consensus of continuous-time multi-agent systems with unbounded and heterogeneous constant delays is investigated by combining frequency-domain analysis and algebraic graph theory. Several types of signed Laplacians are constructed to characterize consensusability under delays. The core results are established based on the defined delay-embedded signed Laplacian, where a small-delay link creates a cooperative interaction and a possibly unbounded large-delay link creates an antagonistic interaction between the agents. The dividing line between small and large delays is given by $τ_{ij}=π/2λ_{\max}(L_0)$, where $λ_{\max}(L_0)$ refers to the maximum eigenvalue of the conventional graph Laplacian. It is proved that the consensusability is preserved if the delay-embedded signed Laplacian is positive semi-definite with a simple zero eigenvalue. Moreover, we derived some consensus conditions in terms of the extended effective resistance which measures the overall coupling between two sets of agents. The obtained results provide new insights into the mechanism of delayed consensus from the interplay between the small-delay-induced cooperativeness and large-delay-induced antagonism in the underlying network topology.
