Rapid transitions are important for quick response of consensus-based, multi-agent networks to external stimuli. While high-gain can increase response speed, potential instability tends to limit the maximum possible gain, and therefore, limits the maximum convergence rate to consensus during transitions. Since the update law for multi-agent networks with symmetric graphs can be considered as the gradient of its Laplacian-potential function, Nesterov-type accelerated-gradient approaches from optimization theory, can further improve the convergence rate of such networks. An advantage of the accelerated-gradient approach is that it can be implemented using accelerated delayed-self-reinforcement (A-DSR), which does not require new information from the network nor modifications in the network connectivity. However, the accelerated-gradient approach is not directly applicable to general directed graphs since the update law is not the gradient of the Laplacian-potential function. The main contribution of this work is to extend the accelerated-gradient approach to general directed graph networks, without requiring the graph to be strongly connected. Additionally, while both the momentum term and outdated-feedback term in the accelerated-gradient approach are important in general, it is shown that the momentum term alone is sufficient to achieve balanced robustness and rapid transitions without oscillations in the dominant mode, for networks whose graph Laplacians have real spectrum. Simulation results are presented to illustrate the performance improvement with the proposed Robust A-DSR of 40% in structural robustness and 50% in convergence rate to consensus, when compared to the case without the A-DSR. Moreover, experimental results are presented that show a similar 37% faster convergence with the Robust A-DSR when compared to the case without the A-DSR.

中文翻译：

---

基于共识网络的具有鲁棒加速延迟自强化的快速转换

快速转换对于基于共识的多智能体网络对外部刺激的快速响应非常重要。虽然高增益可以提高响应速度，但潜在的不稳定性往往会限制最大可能的增益，因此，会限制转换期间达成共识的最大收敛速度。由于具有对称图的多智能体网络的更新律可以被认为是其拉普拉斯势函数的梯度，因此优化理论中的 Nesterov 型加速梯度方法可以进一步提高此类网络的收敛速度。加速梯度方法的一个优点是它可以使用加速延迟自强化 (A-DSR) 来实现，它不需要来自网络的新信息，也不需要修改网络连接。然而，加速梯度方法不能直接应用于一般有向图，因为更新定律不是拉普拉斯势函数的梯度。这项工作的主要贡献是将加速梯度方法扩展到通用有向图网络，而无需图强连接。此外，虽然加速梯度方法中的动量项和过时的反馈项通常都很重要，但表明仅动量项就足以实现平衡的鲁棒性和快速过渡，而不会在主导模式下振荡，对于网络图拉普拉斯算子有实谱。提供了仿真结果来说明所提出的 Robust A-DSR 的性能改进，结构稳健性提高了 40%，共识收敛速度提高了 50%，与没有 A-DSR 的情况相比。此外，实验结果表明，与没有 A-DSR 的情况相比，使用 Robust A-DSR 的收敛速度类似 37%。