Research On Cluster Consensus Of A Class Of Nonlinear Multi-agent Systems

Multi-agent systems are usually composed of multiple subsystems with indepen-dent computing,sensing,and communication capabilities.They are highly flexible,scalable,and fault-tolerant,and have great application prospects in unmanned aerial vehicles,distributed sensor networks,intelligent robotics,and micro-satellite networks.Cluster consensus of multi-agent systems studied in this paper is a new research hotspot in recent years.Unlike the common complete consensus,the relationship between dif-ferent agents may be cooperative or competitive,and the whole system is finally divided into multiple clusters under the action of controller.Eventually,agents in the same clus-ter will reach consensus,while agents in different clusters remain separated.In fact,the phenomenon of cluster consensus exists widely in nature and human society,and has potential application prospects in various scientific fields.However,due to the existing of competitive relationship between agents,the previous complete consensus theory can not be directly applied to cluster consensus problem.Based on the existing research,this paper investigates the cluster consensus of a class of nonlinear multi-agent systems.The main contents are as follows:First,we consider the cluster consensus problem of first-order nonlinear multi-agent systems with directed topology.Nonlinear distributed adaptive controllers are designed for first-order nonlinear systems with and without disturbance using the leader-following approach,and some sufficient conditions are proposed to guarantee the real-ization of cluster consensus.The results show that the topology structure of multi-agent systems and the coupling strength within cluster play a key role in the process of clus-tering.In addition,most of the existing research designed linear controllers and the nonlinear functions in dynamic equations of systems are required to satisfy global Lips-chitz conditions,which limit the application of controllers.However,it is worth noting that the controllers designed here only require the nonlinear functions of systems are continuously differentiable.Second,cluster consensus of second-order nonlinear multi-agent systems with di-rected topology is considered.Linear distributed controllers with simple structure are designed for second-order nonlinear systems satisfying special conditions.Next us-ing the similar idea used in first-order systems,distributed controllers based on relative state information are proposed for second-order systems without and with external dis-turbance by choosing appropriate Lyapunov functions.The parameter estimation in controller is bounded,and nonlinear functions in systems are also only required to be continuously differentiable.Subsequent numerical simulation examples verify the va-lidity of relevant theoretical results.Finally,cluster consensus of second-order nonlinear multi-agent systems based on relative position is studied.Since the speed information of the system may be not avail-able or accurate,the state observer and distributed controller are designed for second-order nonlinear multi-agent systems using the relative position information.Theoretical analysis and simulation results show that multi-agent systems can achieve cluster con-sensus under the action of the controller.