Event-triggered Bipartite Consensus For Multi-agent Systems With Integrator Dynamics

In recent years,with the rapid development of science and network,the potential of applications of multi-agent systems have been explored,and more and more researchers have devoted to the research of this field.The huge applications of multi-agent systems contain industrialization,biology,mathematics,computer science and technology and so on.Among these topics and applications,the research of consensus for multi-agent systems is a very important theoretical branch and the consensus problem has already become the basis theory of agents collaboration between each other in the multi-agent systems.The consensus problem we discuss involves such cases that all the agents in the system convert to a consistent state by the local communication between each other in the absence of the global information of the system.In the research of consensus theory,researches use the graph topology to represent the communication relationship between the agents in the multi-agent systems and the different topologies can obtain different consensus states.Based on this,researchers find that the multi-agent systems with balanced weighted signed graph topology can get bipartite consensus under the consensus control input.While,when the bipartite consensus algorithm is used in the digital platforms,the typical control method is periodic sampling which usually suffers from the limited resources of the hardware and software in the agents.Starting from this,this dissertation will introduce the distributed event-triggered control into the bipartite consensus of the first-order and second-order multi-agent systems over signed graph topology,and design the triggering functions such that the systems can get bipartite consensus when the topology is balanced undirected signed graph and balanced strongly connected directed signed graph,respectively.Also,we get analysis of the stability of the systems.At first,this dissertation introduces distributed event-triggered control for bipar-tite consensus of multi-agent systems over signed graph topology and design the trigger function.We discuss the multi-agent systems with strongly connected directed graph and undirected graph respectively.When we choose the suitable parameters,the sys-tems can reach bipartite consensus and avoid Zeno behavior under the distributed event-triggered control input and trigger funciton.In the analysis,the gauge transformation is used to handle the different signs in the bipartite graph;Meanwhile,we use the measure-ment error to design the event-trigger function such that when the measurement error reaches the given threshold,the agents update their control inputs and the measurement errors reset to zero.At the same time,we add a judging condition for each agent in the algorithm which can ensure that the system does not exhibit Zeno behavior.Second,we get preliminary exploration on the bipartite consensus for the second-order multi-agent systems.We give the mathematical model and the control input for the second-order multi-agent systems under the signed graph topologies,meanwhile,we use the distributed event-triggered control in the second-order systems.When the topology is undirected signed graph,the trigger function we design can guarantee that the system can get bipartite consensus in the given range avoiding Zeno behavior under the suitable parameters.While,when the topology is strongly connected directed signed graph,thinking of the complexity of the second-order multi-agent systems,the trigger function we design can make the system get bipartite consensus and ensures that there exists at least one agent can avoid Zeno behavior.Finally,we have summarized all the results in this dissertation,and discussed the future applications of event-triggered control in the control of multi-agent systems.We also discussed the directions and the future development of the research of consensus algorithm.