Lyapunov stability and precise control of the frictional dynamics of a one-dimensional particle array

Yi Guo, Zhihua Qu, Zhenyu Zhang

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

Using Lyapunov theory and numerical simulations, we analyze the local stability of an array of mechanically coupled particles whose frictional dynamics is described by the Frenkel-Kontorova model, and design feedback controls to precisely control the friction. We first establish the asymptotic stability of the system around the equilibrium positions of the particles. We then show how to construct efficient feedback control laws to achieve any predestined average velocity of the particle array, with no fluctuation, and irrespective of the detailed nature of the interparticle coupling. These rigorous results are supported in extensive numerical simulations, and are expected to be applicable to other related physical systems as well.

Original languageEnglish
Article number094118
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume73
Issue number9
DOIs
StatePublished - 2006

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