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Non‐Lipschitzian control algorithms: application to a nanofriction model
Author(s) -
Protopopescu Vladimir,
Barhen Jacob,
Amselem Gabriel,
Dahan Julien
Publication year - 2006
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.674
Subject(s) - robustness (evolution) , mathematics , scope (computer science) , dimension (graph theory) , feedback control , dynamical systems theory , control theory (sociology) , variety (cybernetics) , scheme (mathematics) , control (management) , mathematical optimization , computer science , mathematical analysis , pure mathematics , artificial intelligence , control engineering , engineering , biochemistry , chemistry , physics , statistics , quantum mechanics , gene , programming language
Recently we proposed a new feedback control algorithm for quantities describing global features of non‐linear dynamical systems. The performance of the algorithm, which is based on the concepts of non‐Lipschitzian dynamics and global targeting, has been successfully demonstrated for systems confined to one spatial dimension and for a specific targeted global quantity, namely the velocity of the centre of mass. In this paper we extend the scope of the non‐Lipschitzian control scheme to multi‐dimensional systems and different targeted quantities. We illustrate the efficiency of the non‐Lipschitzian feedback w.r.t. the ordinary (Lipschitzian) feedback, as well as the robustness and accuracy of the algorithm in a broad variety of control scenarios on the 2‐d Frenkel‐Kontorova model for nanofriction. Published in 2005 by John Wiley & Sons, Ltd.