Formation-Containment Control of Euler-Lagrange Systems of Leaders With Bounded Unknown Inputs.

Motivated by the promising applications of multiple Euler-Lagrange (EL) systems, we study, in this article, the formation-containment (FC) control problem for multiple EL systems of leaders with bounded unknown control inputs and with communication among each other over directed topologies, which can cooperatively generate safe trajectories to avoid obstacles. Given the FC shapes, an algorithm is first proposed to obtain the stress matrix while satisfying certain conditions, based on which a novel adaptive distributed observer to the convex hull is proposed for every follower. An adaptive updating gain is applied to make the observer fully distributed without using the global information of the graph, and a continuous function is designed to restrain the influence of the inputs of the leaders. Then, a local control law using the adaptive distributed observer is presented to accomplish the FC control of EL systems. Based on the Lyapunov stability theory, it is proved that the FC error can be designed as small as possible by adjusting some parameters in the observer.