Adaptive Fuzzy Fixed-Time Formation-Containment Control for Euler-Lagrange Systems

This article studies the fixed-time formation-containment control problem for a group of Euler-Lagrange (EL) systems with unknown disturbances. A layered control-oriented framework, composed of leader formation layer and follower containment layer, is constructed to realize the formation-containment (FC) performance. Firstly, two novel distributed fixed-time estimators with/without time-varying formation variables are developed to obtain the ideal position and velocity for each agent in the two layers, respectively. Then, an improved adaptive integral sliding mode disturbance observer (AISMDO) with reconstructed errors is established to obtain the estimation of external disturbances, which shows less conservatism and provides better estimation performance. Furthermore, considering the potential collisions among agents and obstacles, two artificial functions are incorporated into the backstepping technique to develop the adaptive fuzzy controller. Theoretical analysis shows that all signals in the closed-loop system are bounded in fixed time. Finally, an illustrative simulation is presented to validate the effectiveness of the proposed theoretical algorithm.