Backstepping-Based Adaptive Cooperative Control For Multiple Euler-Lagrange Systems Under Unknown Harmonic Disturbances

This paper studies cooperative control problem for multiple Euler-Lagrange systems with unknown harmonic disturbances, where the disturbances are the superposition of sinusoidal components with unknown amplitude, phase, and frequency. A novel adaptive disturbance observer without requiring the disturbance frequency information is designed to estimate the disturbances. Over the directed network topology, a cooperative control scheme is proposed based on backstepping techniques, so that the tracking error is ultimately uniformly bounded. The scheme developed can be used to reject the harmonic disturbances in a uniform way, which means the characteristics of the disturbances can be described as a fixed parameter vector. Finally, an application is presented to demonstrate the effectiveness of the proposed control strategy in the context of a two-link manipulator system.