Structure-free containment control for uncertain underactuated multiple Euler-Lagrange systems

This article studies the problem of structure-free distributed containment control for uncertain underactuated multiple Euler-Lagrange systems(MELSs) considering disturbances by using a layered approach. First, the second layer is the virtual layer constructed artificially for hierarchical control. We move all virtual nodes to the convex hull formed by leaders in the first layer by implementing containment control algorithms on all virtual nodes. Then, the third layer is the following layer, and we propose an adaptive robust tracking controller to ensure that each follower in the third layer tracks the corresponding virtual node in the second layer. So far, the underactuated MELSs can achieve containment control. Furthermore,through the theoretical derivation, sufficient conditions are obtained to achieve the objective of structure-free containment control. Finally, the effectiveness of the proposed stratified structure-free containment control method is verified by a simulation example.