Stabilization and tracking control of friction dynamics of a one-dimensional nanoarray

Friction can be manipulated by applying perturbations to accessible elements of a sliding system. The dynamics of a one dimensional nanoarray is described by a set of coupled nonlinear equations. We discuss the feedback control problem of the nano particle dynamics that is subjected to a simple periodic form of the substrate potential and linear inter-particle forces. Specifically, we design two control laws which render the closed-loop system globally asymptotically stable and globally tracking any constant velocity respectively. The controls are functions of physically accessible variables, the position and velocity of the center mass of the nanoarray. Simulations show satisfactory closed-loop responses.