Arbitrary-Order Distributed Finite-Time Differentiator for Multi-Agent Systems

TL;DR

This paper introduces a novel arbitrary-order distributed finite-time differentiator for multi-agent systems, enabling followers to estimate derivatives of output information in finite time using only local output data.

Contribution

It proposes a new differentiator design that works under directed graphs and only requires local output information, extending to both relative and absolute output data.

Findings

The differentiator achieves finite-time convergence.

Simulation results verify effectiveness.

Applicable to directed multi-agent systems.

Abstract

This paper proposes arbitrary-order distributed finite-time differentiator (AODFD) for leader-follower multi-agent systems (MAS) under directed graph by only using relative or absolute output information. By using arbitrary-order distributed finite-time differentiator via relative output information (AODFD-R), each follower agent can obtain the relative output information between itself and leader and the relative output's arbitrary-order derivatives, where the information to be measured is only the local relative output information between each follower agent and its neighboring agents. As a simple extension of AODFD-R, the arbitrary-order distributed finite-time differentiator via absolute output information (AODFD-A) is also given. The finite-time stability of the closed-loop system under AODFD is proved by constructing a Lyapunov function skillfully. Finally, several simulation examples are given to verify the effectiveness of the AODFD.