Non-Lipschitzian control algorithm for a 2d nanofriction model

Vladimir Protopopescu, Jacob Barhen, Gabriel Amselem, Julien Dahan

Research output: Contribution to journalArticlepeer-review

Abstract

We present a new feedback control algorithm for quantities describing global features of nonlinear dynamical systems. The algorithm, which is based on the concepts of non-Lipschitzian dynamics, is first analyzed in a general multi-dimensional framework for various targeted quantities and control scenarios. For all these situations we derive the linear stability of the targeted trajectory and show that the time needed to reach it is finite. Thus we underscore the efficiency and robustness of the non-Lipschitzian feedback with respect to the ordinary (Lipschitzian) feedback. We illustrate the algorithm on the 2d Frenkel-Kontorova model for nanofriction.

Original languageEnglish
Pages (from-to)139-148
Number of pages10
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume340
Issue number1-4
DOIs
StatePublished - Jun 6 2005

Funding

This research was sponsored by the Division of Materials Sciences and Engineering, US Department of Energy, under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.

Keywords

  • Frenkel-Kontorova model
  • Global targeting
  • Nanofriction
  • Non-Lipschitzian control

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