Distributed finite-time containment control for multiple Lagrangian systems

Distributed finite-time containment control for multiple Lagrangian systems is addressed by introducing fractional-order powers in the control laws properly. When there exist multiple stationary leaders, we propose a model-independent control law to guarantee that the states of the followers converge to the stationary convex hull formed by those of the leaders in finite time by using both the one-hop and two-hop neighbors´ information. When there exist multiple dynamic leaders, a distributed sliding-mode estimator and a non-singular sliding surface were given to guarantee that the states of the followers converge to the dynamic convex hulls formed by those of the leaders in finite time. We also explicitly show the finite settling time.