Partial Component Consensus Of Multi-agent Systems On Two-layer Networks

Multi-layer network is one of the most advanced research directions in the field of complex network dynamics.Many researchers are interested in the synchronization and consensus of multi-layer network.As the most basic form of multi-layer network,the two-layer network considering the interaction within each layer of multi-agent systems and the interaction between two-layer multi-agent systems.Compared with the single-layer network,the two-layer network is more consistent with the topological characteristics of some complex multi-agent systems.Therefore,it is necessary to study the partial component consensus of multi-agent systems on two-layer networks.However,the research achievement of partial component consensus problem on the two-layer network has not been published yet.In this thesis,the partial component consensus of multi-agent systems in double-layer networks is studied,and a pinning controller and a periodic event trigger controller are constructed successively to achieve partial component consensus of multi-agent systems in double-layer networks.Partial component consensus refers to the convergence of some components of all state variables in a multi-agent system when the time tends to be positive infinite,which is a weaker dynamic behavior than identical consensus.In the third chapter,the first-order leader-follower multi-agent system is extended to the two-layer network.On this basis,two appropriate pinning controllers are constructed respectively,and the corresponding error system is obtained.Then,by using the matrix theory and the stability theory,the partial component consensus problem of the system is transformed into the partial argument stability problem of the error system.A sufficient condition for the two-layer leader-follower multi-agent system to achieve partial component consensus is derived.Finally,numerical simulation verifies the correctness of the theoretical results.As a mechanism combining periodic sampling and event triggering control,periodic event-triggering mechanism has a positive lower bound between any two trigger moments,so as to avoid Zeno phenomenon.Chapter 4 of this thesis extends the first-order leader-follower multi-agent system on single-layer network to two-layer network.On this basis,two appropriate event-trigger controllers are constructed respectively,and the corresponding error systems are obtained.Then,by using matrix theory and stability theory,the partial component consensus problem of the system is transformed into the partial argument stability problem of the new error system,and the sufficient conditions for the two-layer leader-follower multi-agent system to achieve partial component consensus are derived.Finally,numerical simulation verifies the correctness of the theoretical results.