Robust tracking control of an array of nanoparticles moving on a substrate

Control of nanosystems with frictional dynamics using feedback control methods is important to a wide range of applications of nanotribology. This paper studies the tracking control problem of an array of nanoparticles moving on a substrate with friction between the substrate and the particles. The major challenges in this problem include 1) nonlinearities and uncertainties in the frictional dynamics and 2) limited availability of measurable states in nanosystems. In this paper, the particle-substrate and interparticle interactions are considered to be unknown and of general dynamic forms. The unknown effect of unmodeled particle dynamics on the dynamics of the center of mass of the array is also considered. A nonlinear identifier is developed to identify this unmodeled dynamics. A feedback controller is developed upon the identifier to control the center of mass of the particles to track a desired trajectory. Boundedness of the closed-loop states and semiglobal asymptotic stability of the tracking error are proved using Lyapunov theory. Numerical simulation results are provided to demonstrate the performance of the developed identification and control laws.