Prescribed-time formation tracking of second-order multi-agent networks with directed graphs

The objective of this paper is to solve the prescribed-time formation tracking problem for the second-order multi-agent network (MAN) with the interaction graph containing a directed spanning tree. By introducing a time-varying function, a novel prescribed-time observer-based control algorithm is presented for driving all the followers to approach a dynamic leader within the prescribed time, which can be pre-specified as a user-designed parameter in the algorithm and is regardless of the initial condition. Especially, the prescribed-time state observer, as an important component of the algorithm, is newly designed to estimate the states of the leader in a distributed manner and also within a user-determined prescribed time. In order to establish the prescribed-time convergence of the closed-loop system in the cascade form, we design a new Lyapunov function candidate and then derive the corresponding sufficient conditions for prescribed-time stability of the error states. Finally, several numerical examples are performed on six agents to verify the effectiveness of the presented algorithm.