Connectivity recovery of multi-agent systems based on connecting neighbor set

This paper investigates robust and fast consensus of multi-agent systems subject to external attacks. The strategy of connecting neighbor set is proposed to recover the connectivity of the resulting interconnected network, to improve the robustness against next external attacks, and to guarantee the fast consensus of the resulting multi-agent systems. Two strategies are provided to optimize the robustness against next external attacks and the convergence speed of achieving consensus, respectively. Meanwhile it turns out that there exists a trade-off between improving the robustness against next external attacks and enhancing the convergence speed of achieving consensus. Several simulations are provided to demonstrate the effectiveness of the theoretical results.