Finite time estimation and containment control of second order perturbed directed networks

In this paper, an efficient architecture is proposed to achieve finite time containment control of second-order perturbed directed networks with the introduction of distributed estimators. Two cases of dynamic leaders with constant velocity and variable velocity are analyzed based on finite time stability theory. In particular, we propose homogeneous and sequential estimators to guarantee accurate desired position and velocity estimation of followers in finite time. Then the accurate estimations obtained are employed to achieve robust finite time containment control. Distributed control protocols are developed by applying homogeneity theory and sliding mode control so as to make followers converge and remain within the dynamic convex hull spanned by the leaders in finite time and suppress perturbation effectively. Finally, several simulation results are presented as a proof of theoretical analysis.