Research On Consensus Algorithm For Multi-agent Systems Based On Graph Signal Processing

In recent years,with the rapid development of computer and network communication technology,the network systems are developing towards to large scale,high complexity and high intelligence.In order to solve the problem of this kind of complex systems,the theory of multi-agent systems has been studied by many experts and scholars,these achievements have been widely used in robot systems,unmanned aerial vehicle formation,wireless sensor network and military fields.The consensus problem is the basis of multi-agent systems collaborative control,the purpose is to design appropriate protocols such that the state value in the system is consistent after the limited exchange of information.When the multi-agent systems performs the task,each agent must reach an agreement on the task in the face of the changes of the environment.Therefore,it is very important to explore the consensus problem of multi-agent systems.The analysis of convergence rate is very important in the consensus control of multi-agent systems.In most engineering system,a fast convergence rate is necessary.In this paper,we focus on how to improve the convergence speed of the consistency algorithm by using graph signal processing as a tool.(1)We propose a novel method for multi-agent systems via super-nodes cooperation,in order to improve the convergence rate of multi-agent systems to achieve consensus.The new algorithm establishes a graph signal model for the multi-agent systems,and selects super-nodes to cooperate in the graph,improve the speed of consensus.Firstly,we select some super-nodes and divide local sets by single-hop sampling algorithm,and nodes in the local set were cooperated.Then the coarsened graph was obtained by edge connection between super-nodes,and the coefficients of the graph filter were designed by the eigenvalues of the Laplacian matrix.Finally,the signal of super-nodes were averaged by iteration of the graph filter,and transmitted to their neighbor nodes,all nodes achieved average consensus.The simulation results show that the algorithm achieves the average consensus at the end,which can significantly improve the convergence speed and reduce the calculation amount compared with the existing methods.(2)Consensus problem can be solved by distributed optimization methods,we proposed the algorithm based on the information fusion of subgraphs.The algorithm establishes a graph signal model for the multi-agent systems,then the consensus problem is formulated into a distributed optimization problem with auxiliary constraints.By using adistributed strategy,the involved large-scale matrix inverse is approximately solved.The proposed algorithm consists of two steps.The first step is local inversion,in specific,a series of small matrices are obtained by projecting the large matrix on all subgraphs and then their inverses are efficiently solved.Then,we use a patch step to fuse all local values for each node,to finally generate an approximate solution to the optimization problem.The distributed algorithm iteratively solves the problem until the values of all nodes reach the average value of the initial signal,i.e.,achieve the consensus.The simulation results show that the algorithm achieves the average consensus with evident less iterations and lower computational cost,as compared with the existing methods.