Research On Consensus Of Multi-agent Networks Based On Differential Privacy

The past several decades have witnessed that the research on the issues of the consensus of distributed collaborative control algorithm in multi-agent systems has been widely applied in various fields.For example,it can be used in the fields such as intelligent robot control,traffic control,resource allocation and so on.The communication process of each agent in distributed consensus algorithm is that each agent exchanges its own state information with its neighbor nodes and receives their neighbors' sates information,then each agent updates its state at the next moment according to the state receiving from the neighbor node,its own current state information and the weight matrix.However,this method of information communication may lead to the appearance some problems.If the communication information contains sensitive private information that needs to be preserved well,the process of communication may lead to the disclosure of the agent's privacy in the end.In order to handle this problem and prevent the occurrence of privacy disclosure,at present,many researchers concentrate on the privacy preserve and obtain great achievements.They have put forward lots of methods to preserve privacy such as:encryption,access control technology,k-anonymity algorithm,associated rules hidden calculation and so on.The appearance of differential privacy method put forward a new way of thinking to solve the problem of privacy disclosure.We can simplify the process of privacy protection as that we transmit part of the information which needs to be protected after adding Laplace noise,then the information which each agent receives from its neighbor is disturbed,which makes the observer who is access of the transmission signal cannot deduce the exact value of each agent.Based on the problems proposed already,in this paper,we mainly research the differential privacy preserve and consensus analysis in multi-agent systems.The main research results and major contributions are summarized as follows:(1)First of all,we study the basic multi agent system average consensus algorithm.We put forward the sufficient and necessary conditions that system need to satisfy if it can achieve the average consensus at last.Then,the details of the security problem of the algorithm is analyzed: the existence of privacy disclosure problem may appear when data information of some agents need to be published in order to study and analyze the states information of agents for some purposes.In order to solve such problems,we use the Laplace mechanism in the theory of differential privacy.Next we introduce the definition of the Hilbert space.Based on the property of Hilbert space,we then introduce a function and combine the function with Laplace noise to describe a new kind of functional Laplace noise.By adding functional noise to the sensitive information,this paper proposes a new average consensus algorithm of differential privacy.The added functional noise needs to be gradually decaying to ensure convergence,and the mathematical expectation of the noise needs to be 0 to avoid affecting the final consensus result.This algorithm can make sure that the privacy of each agent is preserved well in the process of achieving consensus.At the same time,the algorithm which has been disturbed to realize privacy preserve can also finally make each agent reach the average consensus and then we calculate the convergence rate of the algorithm.It is concluded that the rate of convergence is related to the selection of adjacent matrix.Next,we proves how the algorithm can realize the purpose of reaching differential privacy preservation in detail.According to the Laplace mechanism and the combined characteristics of differential privacy,the level of privacy protection and the sensitivity of the system are obtained,which is extremely vital to this paper.Finally,two simulation results are listed to verify the validity and the efficiency of the main results.Then we compare the effects of the selection of different parameters on the final average consensus and the degree of privacy protection.(2)With regard to the optimization consensus algorithm research,this paper firstly put forward a constrained optimization problem in multi agent network.Then we propose a distributed optimization consensus algorithm based on zero gradient sum to solve the constrained optimization problem mentioned above.The initial value of each agent is the optimal value of each single agent.To obtain the entire system optimal value,on the basis of the property of zero gradient sum,we obtain the conclusion that the optimal value of algorithm is associated with the initial value of each agent and all of the agents in the system can finally converge to same optimal value gradually,which is affected by the choice of cost function in constrained optimization algorithm.Next,we put forward the fact that the privacy disclosure problem will appear with this optimization algorithm when part of agent information is published and we then analyze the reason for the occurrence of this problem.We take the Laplace mechanism in different privacy framework to deal with the problem.Here we also use the functional Laplace noise for its advantages to disturb the final publishing information.Then we propose a multi agent optimization consensus algorithm based on zero gradient sum.It is mentioned that,after the addition of noise,the gradient sum in the algorithm remains equal to 0,so that the final optimization consensus of the system will not be affected a lot,and the system can still achieve the optimization consensus.By structure the Lyapunov function while analyzing the property of convex function,we analyze the convergence of the system,it is remarkable that the system can still achieve the same optimization.The optimal value is also related to the initial value which is similar to the initial algorithm.At the same time,the convergence rate is also calculated.Then the advantages of functional noise in the system are analyzed.The privacy protection level and sensitivity are obtained according to the mapping property of functional noise.Finally,the correctness of the mainly theoretical results is verified by numerical simulation.