Research On Bipartite Consensus For Multi-Agent Systems Under Malicious Attacks

In recent decades,the consensus problems of multi-agent systems are of great academic vitality,mainly owning to its wide applications in various areas such as distributed computing,formation control and wireless sensor network.During the research of multi-agent system,for a long time,cooperation is the only considered relationship between agents.While competition relationship is common in real world multi-agent systems.Research on consensus and its security problem when antagonistic interactions exist is still in its infancy.By proposing resilient bipartite consensus algorithm,this paper addresses the problem of resilient bipartite consensus for multi-agent networks in the presence of misbehaving nodes.Firstly,an overview of the state of the art about the consensus problem of multi-agent systems is provided,which includes the origins of the multi-agent concept and the consensus concept.Then after showing some research results of serveral hot research fields of consensus problem of multi-agent systems,some deficiencies of these researches are analyzed,especially for the case when antagonistic interactions exist.Secondly,a secure bipartite consensus algorithm is proposed targeting the possible Byzan-tine attacks.The main idea of this algorithm is that each normal node removes the extreme values with respect to its own value,and the rest of the values are used for updating its current value.Then,the necessary and sufficient conditions for the system to achieve bipartite consensus are given and proved combining with the network robustness and the concept of structural bal-ance,i.e.,all normal nodes reach resilient bipartite consensus if the associated signed digraph is structurally balanced and has sufficient connectivity in terms of robustness.And four numerical examples are provided to illustrate the developed results.Thirdly,based on the algorithm proposed in the previous work,a new version of secure bipartite consensus algorithm is proposed considering the objective factor of communication delay in the system.The algorithm considers that the acquired information is delayed,i.e.,it is not the current state information of its neighbors.After removing the most extreme information in the obtained delayed information from its neighbors,the remaining information is used for updating its own state.Then the result,which is given and proved using Proofs by Contradiction,shows that all normal nodes reach resilient bipartite consensus if the associated signed digraph is structurally balanced and has sufficient connectivity in terms of robustness.Finally,four numerical examples are provided to illustrate the developed results.Finally,by introducing the quantizer,the information flow in the multi-agent system is tran-fered into quantized information,and thereby the system overhead can be reduced.Based on the main idea of the proposed algorithms in the above work,the secure bipartite consensus algorithm under quantized communication is proposed combining with a local communication strategey.Then,the necessary and sufficient conditions for the quantized system to achieve bipartite consen-sus are given and proved by constructing and analyzing the properties of the Lyapunov function.The result shows that,using quantized communication,all normal nodes reach resilient bipartite consensus if the associated signed digraph is structurally balanced and has sufficient connectivity in terms of robustness.Finally,the effectiveness of the algorithm is verified by four comparative simulation experiments.This paper have made some profitable searches and practices in the consensus problem of multi-agent system when antagonistic interaction exists.The necessary and sufficient condi-tions for the multi-agent system to achieve bipartite consensus in serveral practical situations are obtained,which provides a reference for solving the security problem of multi-agent systems.Therefore,this research has certain theoretical value and practical significance.