Controllability Of Multi Agent Systems Via Pinning Control

A multi-agent system is a group of dynamical systems connected via a network.From the view of mathematical models, a multi-agent system is a system of differen-tial or difference equations with a graph structure. The control theory of multi-agent systems has a practical background of wide applications,such as cooperation of robot-s, formation of unmanned aerial vehicles and attitude synchronization of satellites.The control theory of multi-agent systems is an expansion of the traditional control theory of control systems, which has been a new research branch addressing graph theory, differential equation theory and control theory.Pinning control of multi-agent systems is to control the collective behavior via controlling some nodes of the whole dynamical network. Controllability is a basic concept of control theory of dynamical systems, which reflects the ability of exter-nal inputs. The controllability problem of multi-agent systems via pinning control is whether the controllability of the whole system can be realized by pinning some nodes,which has been a research focus in the recent years.In this thesis, the obtained main results are on the controllability problem of multi-agent systems via pinning control. First of all, a general form of the mathe-matical model on pinning control is established, which includes the existing results as special cases. Some existing results have been extended to the general model. A necessary condition and a sufficient condition for controllability under pinning con-trol are obtained. For some special networks, such as cycle, star, complete graphs and Petersen graph, pinning controllers are constructively designed and controllability is proved for different cases.