Single particle dynamics and control in a sliding nanocluster system

We discuss single particle stability in a sliding nanocluster system represented by the Frenkel-Kontorova model. Both open-loop and closed-loop stability is studied using Lyapunov theory based methods. The systems are used to describe the frictional dynamics of a one-dimensional particle array sliding on a surface, which is subject to two potentials, namely, the substrate-particle and the inter-particle potentials. Average control can be applied to the system to control frictional properties in a desired way. We reveal that single particles are locally stable in the open-loop system without external forces. We also derive sufficient conditions so that the system under the average control law can be asymptotically stabilized. Simulation results are shown to verify the theoretical claims.