Research On Bipartite Consensus Of Multi-agent System Based On Privacy-preserving

Multi-agent systems have become a hot subject in the field of control science,and distributed cooperative control is one of the most important research directions in this field.Consensus control is one of the basic problems in the field of cooperative control of multi-agent systems.Most of the existing work related to the consensus of multi-agent systems is based on the cooperation between agents,specifically,the edge weight of the network is nonnegative.However,in many practical cases,there may be hostile interaction or untrustworthy relationship between agents.Therefore,a signed graph is used to describe a multi-agent system with cooperative and competitive relationship,and its weight may be positive or negative.For this kind of network,it can be called cooperative-competitive network.For cooperative-competitive networks,consensus control makes the final states of all agents tend to two opposite values,which is called bipartite consensus.The existing researches seldom consider the privacy-preserving of agents in cooperativecompetitive networks.Due to the possibility of explicit interaction between agents and hostile agents,if cooperative nodes fully share the known information,then all nodes in the network will no longer have secrets.Therefore,the following three methods are proposed to achieve bipartite consensus privacy-preserving as follows.A Paillier homomorphic encryption algorithm is applied to multi-agent systems,and an encryption interaction protocol is proposed.In this protocol,each node generates only one random number at the same time.When interacting with competing nodes,the edge weight of two nodes is the opposite number of two random numbers.Because the random number of each node is confidential to other nodes,it can effectively protect the privacy of the initial state of agents in cooperative-competitive networks.At the same time,the designed cryptographic interaction protocol does not affect the bipartite consensus of the system.On the basis of the first approach,in order to further prevent the initial state privacy of nodes from being inferred by more than two collusive hostile nodes,an improved encryption interaction protocol is developed.In this protocol,each node generates multiple random numbers and each random number corresponds to each hostile node connected by the node.There is no correlation between the random numbers used by the node and each hostile node in information interaction.Therefore,the designed encryption interaction protocol can hide the initial state and intermediate information of the nodes in a number of collusive hostile nodes,which ensures that the studied system eventually converges to the bipartite consensus of the initial state,and also ensures the privacy of the system.Finally,the accuracy of the two encryption interaction protocols is verified by simulation examples.The classic distributed control model is used as a consensus control strategy.An effective control protocol is designed to exchange noise values and preserve privacy.For the signed weighted connected graph,the initial state is updated and the new initial value is obtained by exchanging the noise value between the cooperative nodes before the information exchange of the whole system,so as to achieve the purpose of hiding the initial state.The consensus algorithm can make the system converge to bipartite consensus and ensure the privacy of the initial state of all agents.Finally,a numerical example is given to verify the effectiveness of the main results.