Non-Lipschitzian control algorithms: Application to a nanofriction model

Recently we proposed a new feedback control algorithm for quantities describing global features of non-linear dynamical systems. The performance of the algorithm, which is based on the concepts of non-Lipschitzian dynamics and global targeting, has been successfully demonstrated for systems confined to one spatial dimension and for a specific targeted global quantity, namely the velocity of the centre of mass. In this paper we extend the scope of the non-Lipschitzian control scheme to multi-dimensional systems and different targeted quantities. We illustrate the efficiency of the non-Lipschitzian feedback w.r.t. the ordinary (Lipschitzian) feedback, as well as the robustness and accuracy of the algorithm in a broad variety of control scenarios on the 2-d Frenkel-Kontorova model for nanofriction.