TY - JOUR
T1 - Lyapunov stability and precise control of the frictional dynamics of a one-dimensional particle array
AU - Guo, Yi
AU - Qu, Zhihua
AU - Zhang, Zhenyu
PY - 2006
Y1 - 2006
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevB.73.094118
DO - 10.1103/PhysRevB.73.094118
M3 - Article
AN - SCOPUS:33645022333
SN - 1098-0121
VL - 73
JO - Physical Review B - Condensed Matter and Materials Physics
JF - Physical Review B - Condensed Matter and Materials Physics
IS - 9
M1 - 094118
ER -