Formation tracking control for multi-agent systems with nonlinear dynamics via impulsive control

In this paper, the formation tracking problem of multi-agent system via impulsive control approach is investigated, where each agent can be modeled as an identical nonlinear oscillator. The impulsive control approach is firstly applied to the study of formation tracking problem in the multi-agent system. The objective of the formation tracking problem is to design the formation tracking protocol such that one agent follows the trajectory of a dynamic leader while also keeps the desired formation pattern with other agents simultaneously. By using properties of the Laplacian matrix and combining the 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. A numerical example is given to illustrate the effectiveness of our theoretical results.