Study On Differentially Private Mean Square Consensus For Second-Order Multi-Agent Systems

In recent years,with the increasing scale of wireless communication networks,the potential risk of private information leakage during wireless communication has attracted more and more attention from researchers.Multi-agent system is a type of distributed system.In order to accomplish the global goal,each agent in multi-agent systems communicates with its neighbors to exchange information.As a classic topic of multi-agent systems,the distributed consensus still does not have a complete privacy protection scheme,especially in second-order multi-agent systems.The transmitted information contains the state information of agents,and if an opponent eavesdrops transmitted information in the communication environment or it is a neighbor of agents,the precise state information of agents is leaked,which may inflict incalculable costs.The existing encryption and decryption schemes could play a role in privacy protection,however,with the development of the opponent’s code-breaking technology,there is still the risk of privacy leakage.For the above problems,this paper proposes a differentially private mean square consensus scheme for second-order multi-agent systems.Then,considering the case that partially measurable states and limited communication environment,this paper proposes a differentially private mean square consensus with quantized communication for secondorder multi-agent systems.The effectiveness of schemes proposed in this paper has been proved,and the experimental simulation cases are designed to visually demonstrate the rationality and effectiveness of the schemes.The research content and primary work involved are as follows:(1)The random variables in differential privacy are the source of the privacy protection effect,and also make the multi-agent system a stochastic system.In this paper,two differentially private mean square consensus algorithms for second-order multi-agent systems are proposed by using exponentially decaying Laplace noise.The author proves the effectiveness of the algorithms.(2)In this paper,the differential privacy is introduced to improve the privacy security of second-order multi-agent systems during communication process.For the differentially private distributed consensus schemes proposed in this paper,author quantifies the privacy protection level of each agent.(3)In the process of distributed consensus,the states of agents are random variables.Therefore,this paper quantitatively analyzes the distribution characteristics of the states of agents and the convergence value of the multi-agent system.(4)Since the quantized communication is affected by random variable in differential privacy,author analyzes the probability relationship between quantizer saturation and memory capacity by using the knowledge of probability theory and matrix theory.