Protocol selection for second-order consensus against disturbance
Jiamin Wang, Liqi Zhou, Dong Zhang, Jian Liu, Feng Xiao, Yuanshi Zheng · Automatica · 2024
Noticing that both the absolute and the 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 L 2 gains from disturbance to consensus errors. More specifically, by the orthogonal transformation technique, the analytic expression of the L 2 gain of a second-order multi-agent system with the absolute velocity protocol is firstly derived, followed by the counterpart with the relative velocity protocol. It is shown that both the L 2 gains for the absolute and the relative velocity protocols are determined only by the minimum non-zero eigenvalues of Laplacian matrices and the tunable gains of position-like and velocity-like states. 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, numerical tests are given for different types of interaction graphs.