Cooperation Control For Networked Complex Dynamic Multi-agent Systems

Complex dynamic networks and multi-agent systems are two popular topics in thestudy of control area. With the development of complex dynamic networks,synchronization has roused lots of researchers’ wide concern, it becomes a hot issue ofcomplex networks. One of the important issues in the multi-agent systems studies is thecoordination control between any two agents, and make multi-agents consensus is thekey to realize coordination control. As we know, there have many research results insynchronization for continuous complex dynamic networks and continuous multi-agentsystems already, however, discrete time system has more extensive applicationbackground. The acting time of discrete system is sampling time, and the system modelis strong uncertainty, so discrete time system is more suitable for practical engineeringapplication. Therefore, synchronization for discrete time complex dynamics andconsensus for discrete time multi-agent systems are valuable researches for us.In light of the above, this paper mainly studies discrete time network systems. Themain contents are as follows:Firstly, the consensus for discrete time leader following multi-agent systems isdiscussed. A distributed learning control law is designed for multi-agent systems infixed topology by iterative learning control, while the initial reset error of system is zero.We obtain sufficient conditions to make sure that all the followers can follow the tracksof the leader in finite time horizon, thus multi-agent systems consensus are derived. Atlast,two numerical examples are provided to illustrate our design.Secondly, based on the previous chapter for studying the consensus of discretetime leader following multi-agent systems with fixed topology, we aim at switchingtopology multi-agent systems in this chapter. A distributed learning control law isdesigned with iterative learning control. What’s more, we designed a distributedlearning law for the initial states to get rid of the initial reset. From this we prove thatthe control law we designed can make the tracking errors asymptotically reach theorigin. Besides, a formation control method for first-order difference system is analyzed.In the end, numerical examples are provided to illustrate the effectiveness of thealgorithms.Thirdly, the synchronization theory of discrete time complex dynamic networks isstudied, and the stability of the network is analyzed with Lyapunov stability method. On the condition that the synchronizing track and topologic information of the complexnetworks are time varying and uncertainty, we designed a fragile feedback controlalgorithm to make the network achieve the global synchronization. In order to achievesynchronization, it’s worth noting that we suppose the coupling configuration matrixand the disturbance of the internal coupling matrix are all bounded.