Adaptive formation-containment control for multiple Euler-Lagrange systems with uncertainties and disturbances

This paper investigates a new kind of cooperative control problem, formation-containment control for multiple nonlinear Euler-Lagrange systems composed of leaders and followers under directed communication topology. The formation-containment control problem is an improvement upon the existing containment control problem in which the states of leaders are assumed to have spanned to a convex hull. First, to make each leader converge to the desired time-varying formation, an adaptive formation control algorithm based on neural-networks is proposed for leader systems with uncertainties and disturbances. Secondly, by designing proper auxiliary variables for follower systems, a distributed containment control law is provided such that all followers converge to the convex hull spanned by the controlled leaders. Finally, a mathematical simulation is given to demonstrate the effectiveness of the control algorithms.