Formation-containment tracking for general linear multi-agent systems with a tracking-leader of unknown control input

This paper investigates the formation-containment tracking problems for general linear multi-agent systems with a tracking-leader of unknown control input, where the agents are classified into a tracking-leader, several formation-leaders and followers. The formation-leaders are required to accomplish a given time-varying formation configuration and track the desired trajectory generated by the tracking-leader simultaneously, while the followers need to converge to the convex hull spanned by the formation-leaders. Firstly, based on the neighboring relative information, a formation-containment tracking protocol is proposed under the influences of the tracking-leader's unknown input. Then an algorithm is given to determine the control parameters, where a general formation-containment tracking feasible constraint is presented. It is proved that the given formation-containment tracking can be achieved under the discontinuous protocol. Furthermore, in order to avoid the large chattering of the control inputs, a continuous formation-containment tracking protocol is also presented, under which the errors can converge to an arbitrarily small neighborhood of zero. Finally, a simulation example is given to verify the theoretical results.