Protocol selection for second-order consensus against disturbance

TL;DR

This paper compares the anti-disturbance capabilities of absolute and relative velocity protocols in second-order multi-agent systems, deriving explicit L2 gain formulas and establishing graph conditions for optimal protocol selection.

Contribution

It provides analytical expressions for L2 gains of both protocols and introduces criteria and a scheme to enhance anti-disturbance performance.

Findings

Both protocols' L2 gains depend on Laplacian eigenvalues and tunable gains.

Graph conditions determine which protocol has better anti-disturbance capability.

A two-step scheme improves the system's robustness against disturbances.

Abstract

Noticing that both the absolute and relative velocity protocols can solve the second-order consensus of multi-agent systems, this paper aims to investigate which of the above two protocols has better anti-disturbance capability, in which the anti-disturbance capability is measured by the L2 gain from the disturbance to the consensus error. More specifically, by the orthogonal transformation technique, the analytic expression of the L2 gain of the second-order multi-agent system with absolute velocity protocol is firstly derived, followed by the counterpart with relative velocity protocol. It is shown that both the L2 gains for absolute and relative velocity protocols are determined only by the minimum non-zero eigenvalue of Laplacian matrix and the tunable gains of the state and velocity. Then, we establish the graph conditions to tell which protocol has better anti-disturbance capability. Moreover, we propose a two-step scheme to improve the anti-disturbance capability of second-order multi-agent systems. Finally, simulations are given to illustrate the effectiveness of our findings.