Tracking control for multiple Lagrangian systems using neural networks without relative velocity information

This paper presents a distributed leader-following control approach for a group of uncertain Euler-Lagrange systems in the absence of the neighbors´ velocity information under an undirected communication graph. We study the dynamic leader case. The Euler-Lagrange systems´ unknown dynamics and external disturbances are compensated by the function approximation technique of neural networks (NN). Combining a kind of low-pass filter with the Lyapunov method facilitates the whole control system design and analysis. A distributed adaptive controller is designed so that the tracking errors of each follower converge to an adjustable neighbourhood of the origin considering unknown dynamics and external disturbances regardless of the lack of relative velocity information. Simulation results are presented to illustrate the effectiveness of the proposed control scheme.