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This article studies the second-order consensus problem in networked systems containing the so-called Byzantine misbehaving nodes when only an upper bound on either the local or the total number of misbehaving nodes is known. The existing results on this subject are limited to malicious/faulty model of misbehavior. Moreover, existing results consider consensus among normal nodes in only one of the two states, with the other state converging to either zero or a predefined value. In this article, a distributed control algorithm capable of withstanding both locally bounded and totally bounded Byzantine misbehavior is proposed. When employing the proposed algorithm, the normal nodes use a combination of the two relative state values obtained from their neighboring nodes to decide which neighbors should be ignored. By introducing an underlying virtual network, conditions on the robustness of the communication network topology for consensus on both states are established. Numerical simulation results are presented to illustrate the effectiveness of the proposed control algorithm.
Koushkbaghi et al. (Thu,) studied this question.