Consensus Of Multi-agent Dynamical Networks

Multi-agent dynamical network system theory is a pioneering research topic of control theory. A multi-agent dynamical network can be described by a undirected graph or a directed graph. Each vertex has a state variable described by a differential equation with a control term (control system)and every edge represents information transition.If there is a directed edge from one vertex to the other, then the later can receive the state of the former, i.e. the control term of the later can use the state information of the former in designing the control algorithm, which is called a dis-tributed control protocol due to that only local information transmitted through the network. The consensus problem of multi-agent dynamical networks is to design dis-tributed control protocols so that all the states of the vertices tend to be in agreement asymptotically. The consensus problem has widespread background of applications, for example, the synchronization of power systems connected by many generators, consensus phenomenon appeared in the collective behaviors of biological flocks and the formation control of a group of robots.In this thesis, two aspects of results are obtained.1) Based on directed graphs with fixed topologies, a Lyapunov method for the consensus analysis is proposed and the consensus convergence speed estimation is given. Furthermore, the obtained results are generalized to the case of a kind of switching topologies. Compared with corresponding existing results, the model discussed here is more general and the switching topology is not a balanced graph.2) Based on proximity graphs, a sufficient consensus condition is proposed for a switching discrete nonlinear multi-agent network. By mathematical induction, the consensus of the closed-loop is proved. Compared with corresponding existing results, a new nonlinear discrete multi-agent model different from the traditional Vicsek model is established. Some results on Vicsek mode are generalized to this new model. A relationship between this new model and a continuous nonlinear multi-agent system is revealed. For the obtained theoretical results, numerical examples and simulations are given.