Formation Control Of Multi-agent Systems By Graph Filtering

The formation control of multi-agent systems has very important theoretical value and application significance.As an important problem in multi-agent systems,formation control has a wide range of applications in the field of biology,automatic control,robotics,artificial intelligence and so on.The goal of formation control is to maintain the desired geometric state(i.e.,formation)of multiple agents in the process of moving to a specific target or direction.The key problem of formation control is how to design an appropriate distributed control algorithm based on local neighbor information so that the multi-agent system can achieve the desired formation.This paper studies the formation control problem of first-order,second-order and third-order multi-agent systems on an undirected network from the perspective of graph signal processing.By introducing the relative position error variables,the formation control problem of the original system is transformed into the consensus problem of the error system.The formation control algorithm is designed by using the graph filtering method.The main research work of this paper is as follows:(1)For the first-order and second-order multi-agent systems,given a known network,a finite-time formation control algorithm is proposed to achieve the desired formation in finite time.In the case of unknown network,a periodic asymptotic formation control algorithm is proposed to achieve the desired formation asymptotically.Finally,the validity of the theoretical results is verified by numerical simulation.(2)For the third-order multi-agent system,given a known network,a finite-time formation control algorithm is proposed to achieve the desired formation in finite time.Finally,the effectiveness of the proposed finite-time formation control algorithm is verified by numerical simulation.