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This work is devoted to a dynamic consensus problem referred here as distributed differentiation, which consists on estimating high order derivatives of the average of a group of signals in a decentralized fashion. To do so, a distributed differentiation protocol is proposed which solves the problem with exact convergence in the noiseless case. Moreover, the protocol allows to compute weighted averages according to quality or noise levels of individual signals. Different from previous approaches, our proposal no longer requires additional local differentiators. In addition, we provide a detailed formal analysis of the performance of the protocol under noisy measurements. Simulation examples are provided to show the effectiveness of our proposal.

This article addresses the problem of average consensus by a multi-agent system when the desired consensus quantity is a time varying signal, in particular the average of individual time varying signals localized at the agents. Although this problem has been addresses in existing literature by linear schemes, only bounded steady-state errors has been achieved. In this work, we propose a new exact dynamic consensus algorithm which leverages high order sliding modes 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. Finally, the effectiveness and advantages of our proposal are shown with concrete simulation scenarios.