Neural network-based distributed consensus tracking control for uncertain Euler–Lagrange systems over directed topologies.

This paper proposes a neural network-based robust control approach for driving disturbed Euler–Lagrange systems (e.g., robot manipulator) in a directed network to perform consensus tracking of a heterogeneous leader's output signal. The parameter matrices and external disturbances in each follower's Euler–Lagrange dynamics are unmeasurable, thus we unify them into one lumped uncertainty term. Neural networks are then employed to online estimate these uncertainties, with adaptive update laws ensuring the boundedness of the estimation errors. Subsequently, a set of distributed observers are developed to adaptively estimate the leader's states as well as the unidentified parameter vector and output matrix in the leader's model. With their help, the robust cooperative controller is designed. Its efficacy on directed networks is theoretically justified by designing a Lyapunov function with a special structure. This function produces symmetric positive definite matrices when its first derivative terms interact with the specified parameters in the observer and Laplacian matrices for directed graphs. Finally, numerical simulations based on two-link robot manipulators are carried out to verify that the tracking errors converge to zero when applying the neural network-based robust controller. [ABSTRACT FROM AUTHOR]