Non-Lipschitzian control algorithm for a 2d nanofriction model

We present a new feedback control algorithm for quantities describing global features of nonlinear dynamical systems. The algorithm, which is based on the concepts of non-Lipschitzian dynamics, is first analyzed in a general multi-dimensional framework for various targeted quantities and control scenarios. For all these situations we derive the linear stability of the targeted trajectory and show that the time needed to reach it is finite. Thus we underscore the efficiency and robustness of the non-Lipschitzian feedback with respect to the ordinary (Lipschitzian) feedback. We illustrate the algorithm on the 2d Frenkel-Kontorova model for nanofriction.