Robust arbitrary trajectory tracking of multiple heterogeneous Euler–Lagrange systems under directed graphs: A fully distributed event-triggered control

In this paper, the robust arbitrary trajectory tracking problem of multiple heterogeneous Euler–Lagrange (EL) systems with disturbances under a directed graph is investigated via a novel fully distributed event-triggered control (ETC) strategy. Firstly, for an arbitrary tracked trajectory, the Fourier transform technique is employed to approximately obtain its linear form, which represents the leader of multiple EL systems. Since the dynamics and state of the leader are not available to all followers, fully distributed adaptive ETC-based observers are proposed for each follower to reconstruct the leader's trajectory, where the global information requirements are avoided, and the Zeno behavior is excluded by giving the minimum triggering intervals. Armed with the observed information, a robust adaptive ETC protocol is further developed such that the position-like state of each follower can track the leader with the intermittent controller updating, where a minimum control update interval is obtained theoretically. Moreover, the adaptive technique is used to eliminate the influence of the parameter uncertainties of multiple EL systems, thus the tracking is achieved asymptotically. Finally, simulation results are illustrated to show the feasibility and effectiveness of the proposed control strategy.