AI 中文总结
研究网络扰动对线性时不变多智能体系统一致性轨迹的影响，通过建立拉普拉斯域准则等方法，揭示经典鲁棒同步存在漏洞，如同步到周期轨迹易被传输延迟破坏，d正则拓扑下传输扰动会使系统同步到新频率，强调需对网络参考生成器进行结构修改。
AI 中文摘要
多智能体系统的分布式协调通常依赖旨在就规定的非平凡轨迹达成一致的协作协议。虽然此类协议对各种不确定性的鲁棒性已有充分记录，但现有文献普遍假设目标一致轨迹本身保持不变。我们证明网络扰动会极大地改变渐近一致轨迹。首先通过建立新的拉普拉斯域准则研究受动态耦合不确定性影响的线性时不变（LTI）智能体的精确轨迹。引入结构保持动力学概念并与仅影响邻接矩阵的传输动力学对比。证明标准协作输出调节方案存在关键脆弱性，如静态共识对异构传输延迟具有独特鲁棒性，但同步到周期轨迹会被任意小的传输延迟破坏。还表明对于d正则拓扑，均匀传输扰动可轻易使系统与意想不到的全新频率同步。这些发现揭示了经典鲁棒同步中先前未识别的漏洞，表明传输动力学需要对网络参考生成器进行根本性结构修改。
英文摘要
Distributed coordination of multi-agent systems frequently relies on cooperative protocols designed to achieve agreement on a prescribed, non-trivial trajectory. While the robustness of such protocols to various uncertainties is well documented, existing literature universally assumes that the target agreement trajectory itself remains invariant. This assumption may hold in ideal cases, but we prove that network perturbations can vastly modify the asymptotic agreement trajectory. We first investigate the exact trajectories of Linear Time-Invariant (LTI) agents subjected to dynamic coupling uncertainties by establishing a new Laplace-domain criterion that characterizes the specific closed-loop poles governing the perturbed agreement manifold. To formalize our analysis, we introduce the notion of structure-preserving dynamics, perturbations that maintain the null space of the communication graph's Laplacian, and contrast them with transmission only dynamics, affecting only the adjacency matrix. We prove a critical fragility within standard cooperative output regulation schemes: while static consensus is uniquely robust to heterogeneous transmission delays, synchronization to periodic trajectories is destroyed by arbitrarily small transmission delays. Furthermore, we demonstrate that for d-regular topologies, uniform transmission perturbations can easily shift the system to synchronize with an unexpected, entirely new frequency. These findings expose a previously unidentified vulnerability in classical robust synchronization, demonstrating that transmission dynamics necessitate fundamental structural modifications to networked reference generators.
Comments12 pages, 9 figures, submitted to IEEE for possible publication
