Resilient Consensus in the Presence of Misbehaving Agents and External Sources

This paper studies the resilient consensus of a multi-agent system in the presence of an external source and misbehaving agents. A dynamic model is considered that integrates an external signal from the source to the weighted-mean-subsequence-reduced (W-MSR) based algorithm. Graphtheoretic conditions for resilient consensus are derived based on a new notion of tier-<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> conformity, ensuring that the consensus value remains independent of the misbehaving agents and is determined by the external signal. For the special case where all agents receive the external signal, exponential convergence to the consensus value is proven. Numerical examples are included to illustrate and validate the theoretical findings.