We present a robust feedback control algorithm and apply it to the nonlinear oscillator array (Frenkel-Kontorova) model of nanoscale friction. The new control approach is based on the concepts of non-Lipschitzian dynamics and global targeting. We show that average quantities of the controlled system can be driven - exactly or approximately - towards desired targets which become additional, linearly stable attractors for the system's dynamics. Extensive numerical simulations show that the basins of attraction of these targets are reached in very short times and the control exhibits very strong robustness. We investigate the efficiency of the control in terms of various parameters (e.g., system size, non-Lipschitzian exponent).