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.

翻译：本条涉及多试剂系统中在所希望的协商一致数量是一个时差信号时的平均共识问题。虽然这个问题已在现有文献中通过线性办法得到解决,但只实现了有条不紊的稳定状态错误。其他方法则使用第一顺序的滑动模式实现零稳定状态错误,但受到抖动效应的影响。在这项工作中,我们建议采用一种新的确切的动态协商一致算法,以分布式差异算法的形式,利用高顺序滑动模式,在一组代理人中实现平均时间差参考信号的零稳定状态错误。此外,我们的提案还能够达成共识,如果需要的话,就平均信号的高顺序衍生物达成共识。对EDCHO的稳定性和趋同性进行了深入的正式研究,对未定向连接的图表进行了研究。最后,我们的提案的有效性和优点以具体的模拟情景显示。