Sufficient and Necessary Condition for Resilient Consensus under Time-varying Topologies

摘要

Although quite a few results on resilient consensus of multi-agent systems with malicious agents and fixed topology have been reported in the literature, we lack any known results on such a problem for multi-agent systems with time-varying topologies. Herein, we study the resilient consensus problem of time-varying networked systems in the presence of misbehaving nodes. A novel concept of joint ($r, s$) -robustness is firstly proposed to characterize the robustness of the time-varying topologies. It is further revealed that the resilient consensus of multi-agent systems under $F$-total malicious network can be reached by the Weighted Mean-Subsequence-Reduced algorithm if and only if the time-varying graph is jointly ($F+1, F+1$) -robust. Numerical simulations are finally performed to verify the effectiveness of the analytical results.