In this paper, we address the problem of steering Lagrange system to track targets with unknown trajectory in the presence of modeling uncertainties and actuation faults. Artificial neural network technique is employed to reconstruct the behavior of the targets with unknown trajectory, with which robust adaptive fault-tolerant tracking control algorithms are developed. The developed control scheme is able to cope with unknown desired trajectory, attenuate modeling uncertainties and accommodate actuation faults. The proposed control scheme is shown to be able to maintain close target tracking despite actuation ineffectiveness and desired trajectory uncertainty. The benefits and feasibility of the developed control are also confirmed by simulations.