Resilient consensus of double-integrator multi-agent systems

We propose an algorithm for consensus of second-order sampled-data multi-agent systems in the presence of misbehaving agents. Each normal agent updates its values (position and velocity) following a predetermined control law based on local information obtained through directed interaction while some malicious agents make updates arbitrarily. The normal agents do not know the global topology of the network, but have prior knowledge on the maximum number of malicious ones. Under the assumption that the network topology has sufficient connectivity in terms of robustness, we develop a resilient algorithm where each agent ignores the neighbors which have large and small position values to avoid being influenced by the malicious agents. The effectiveness of the approach is demonstrated through a numerical example.