Group Consensus Of Heterogeneous Multi-agent Systems Based On Complex Frequency Analysis

Since multi-agent systems(MASs)has extensive potential application in unmanned aircraft,pattern recognition,robots,network information security,and artificial intelligence control,it has been received much attention and in-depth research by many scholars.As one of a hot topic,control of group consensus has attracted the interest of many researchers and a lot of related results have been obtained.However,most of the obtained results are only under the assumption that the agents are homogeneous,the topological structure of multi-agent systems is connected(the minimum spanning tree exists)or the input and output degrees are balanced,and the relation between the agents is only competitive or cooperative.Compared with actual problems,these conditions are too limited.On the basis of existing results,this paper has deeply investigated the group consensus of continuous and discrete heterogeneous multi-agent systems based on competitive-cooperative relationship and complex frequency analysis theory,some achievements have been obtained as follows.First,a new weighted group consensus protocol is proposed for a class of continuous heterogeneous multi-agent systems.In this novel protocol,positions,speed,competitive-cooperative relationship,self-adaptive controller,communication and input delay are all considered.Based on graph theory,Laplace transform method and linear algebra theory,some sufficient conditions have been obtained to realize the weighted group consensus of this system.According to these sufficient conditions,if the weighted parameters meet with these sufficient conditions,the upper limit of time delay of the multi-agent systems can be calculated according to the given parameters.These sufficient conditions also show that the realization of group consensus is only related to the input delay and it has not related to the communication delay.These conclusions are not only applicable to heterogeneous multi-agent systems with undirected topology,but also they are suitable for the directed heterogeneous multi-agent systems.Finally,several numerical experiments have verified the correctness of the relevant theoretical results.Secondly,similar to the control of group consensus of continuous heterogeneous multi-agent systems,a new weighted grouping consensus protocol has been put forward for a kind for a discrete heterogeneous multi-agent systems based on self-adaptive control and cooperative-competitive interaction.By using the z-transform method,Euler formula,disc theorem,matrix analytical theory and graph algebra theory,some sufficient conditions have been also given to realize the group consensus of this system.These sufficient conditions are not only suitable for the system with undirected topological structures,but also they are suitable for the system with directed topological structure,and there is no need to meet with the balance condition of in-out degree.Similarly,the maximum input delay of the system can be calculated according to the weighted parameters and sufficient conditions,and the realization of group consensus is only related to the input delay,and it is not related to the communication delay.The communication delay only affects the speed of realizing group consensus.Numerical experiments have shown the validity of the relevant conclusions.