Finite-time formation-containment tracking for second-order multi-agent systems with a virtual leader of fully unknown input

Abstract

This paper studies the finite-time time-varying formation-containment tracking problems for second-order multi-agent systems with directed topology, where the multi-agent system consists of one virtual leader with fully unknown input, several real leaders and followers. In contrast with traditional formation and containment cases studied in most of the existing literature, apart from accomplishing the expected time-varying formation, the real leaders are required to track the trajectory generated by the virtual leader, and the followers need to get into the convex envelope spanned by the real leaders in finite time. The method for solving the finite-time formation-containment tracking problems is divided into the following steps. First, distributed finite-time observers are designed for each real leader and follower, in order to obtain the estimated states of their neighbor agents. Then, formation-containment tracking protocols are presented by using the neighboring information for both real leaders and followers. Furthermore, based on Lyapunov theory, it is proved that the given formation-containment tracking can be realized in finite time by the multi-agent system under the designed protocols. Finally, a case study on multi-robot transport operation is given to verify the effectiveness of the theoretical results.