Synchronization in the Frenkel-Kontorova Model with Application to Control of Nanoscale Friction⁎The research was funded by the Czech Science Foundation (GACR) under contract No. 21-07321S. Issue 14 (2021)

• Record Type: Journal Article
• Authors: Do, Loi; Hurák, Zdeněk
• Is Part Of: IFAC-PapersOnLine. Volume 54:Issue 14(2021)
• Page Start: 406
• Page End: 411
• Publication Date: 2021
• Subjects: Frenkel-Kontorova model -- multi-agent system -- synchronization -- nanoscale friction; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2021.10.388
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: This paper tailors synchronization of multi-agent systems to motion control of the Frenkel-Kontorova (FK) model, a one-dimensional chain of harmonically coupled identical particles in a spatially periodic potential field. In particular, the goal is to drive all particles in the FK model to the desired trajectory by controlling only a single—boundary—particle. The proposed solution augments harmonic coupling in the FK model with dissipative inter-particle interactions, allowing all particles in the chain to synchronize to a particular reference trajectory. The boundary control represents a special case of pinning control. Moreover, as the FK model describes the frictional dynamics of a nanosheet sliding over a surface, we use its synchronization for controlling the nanoscale sliding friction. The key idea is to introduce a sliding reference trajectory that allows particles to move near synchrony. Synchronization effectively increases the system's stiffness, so less energy ends up dissipated through inter-particle relative motion, thus reducing the frictional force. We validate the proposed solution through numerical simulations.