The Study Of Impulsive Formation Tracking Problems In Multi-agent Systems

In recent years, formation control is attracting more and more attention and becoming one of the hot topics in the coordination control of multi-agent system as its wide range of applications. Formation control is to keep in the certain formation to achieve the goal, formation control with a group reference, called formation tracking, refers to the same task but following the pre-designed group reference. Roughly speaking, the formation tracking control algorithms are designed and based on algebraic graph theory, matrix theory, stability theory of impulsive system, such that a group of agents maintain the predesigned formation and follow the trajectory of the leader. The main contents of this thesis are summarized as follows.The formation tracking problem of first-order multi-agent system via impulsive control approach is investigated. By using properties of the Laplacian matrix, and combining algebraic graph theory, matrix theory, stability theory of impulsive systems and the concept of “average impulsive interval”, sufficient conditions are given to guarantee the formation tracking of the multi-agent system.The formation tracking problem for the second-order multi-agent system with and without input delay via impulsive control are investigated, respectively, in which both the directed graph and undirected graph are considered. The main contributions are as follows: only the velocity is regulated by the control force, the algorithms are designed by using relative position-only information and both the cases with and without input delay are considered. By using properties of the Laplacian matrix and combining algebraic graph theory, matrix theory, and the stability theory of impulsive systems, necessary and sufficient conditions are derived for the cases with and without the input delay, respectively.Finally, a summary has been made and the further studies are presented for the formation tracking of the multi-agent systems in the thesis.