This article addresses the problem of average consensus in a multi-agent system when the desired consensus quantity is a time varying signal. Although this problem has been addressed in existing literature by linear schemes, only bounded steady-state errors have been achieved. Other approaches have used first order sliding modes to achieve zero steady-state error, but suffer from the chattering effect. In this work, we propose a new exact dynamic consensus algorithm which leverages high order sliding modes, in the form of a distributed differentiator to achieve zero steady-state error of the average of time varying reference signals in a group of agents. Moreover, our proposal is also able to achieve consensus to high order derivatives of the average signal, if desired. An in depth formal study on the stability and convergence for EDCHO is provided for undirected connected graphs. Finally, the effectiveness and advantages of our proposal are shown with concrete simulation scenarios.

本文解决了当所需的共识数量是随时间变化的信号时，多智能体系统中的平均共识问题。尽管该问题已在现有文献中通过线性方案解决，但仅实现了有界稳态误差。其他方法使用一阶滑动模式来实现零稳态误差，但会受到颤振效应的影响。在这项工作中，我们提出了一种新的精确动态一致性算法，该算法以分布式微分器的形式利用高阶滑动模式在一组代理中实现时变参考信号平均值的零稳态误差。此外，如果需要，我们的提议还能够就平均信号的高阶导数达成共识。为无向连通图提供了对 EDCHO 稳定性和收敛性的深入正式研究。最后，通过具体的模拟场景展示了我们建议的有效性和优势。