Secure multi-dimensional consensus algorithm against malicious attacks

Abstract

In this paper, we investigate the problem of multi-dimensional consensus subject to the internal agent dynamics constraint and external non-cooperative malicious attacks. We propose a secure discrete-time multi-dimensional consensus algorithm (SMCA), where two-hop information is utilized to check the integrity of neighboring agents’ information. Furthermore, we derive a necessary and sufficient condition for all normal agents to achieve consensus exponentially under SMCA. For the boundary-case attacks under SMCA, we first cast the problem as an equivalent problem of multi-dimensional consensus with nonuniform time-delays, and then obtain the analytical expression of the attacks’ effects on the final state and convergence rate. Compared with the existing works, SMCA can achieve multi-dimensional consensus for all normal agents with local dynamics even when the number of compromised agents is unknown. Finally, extensive simulations demonstrate the effectiveness of the proposed algorithm.