TY - JOUR
T1 - On the algebraic reconstruction of the Duffing's mechanical system
AU - Aguilar-Ibanez, Carlos
AU - Sanchez H., Jorge H.
AU - Suárez C., Miguel S.C.
AU - Martinez C., Juan
N1 - Funding Information:
This research was supported by the Secretaria de Investigación y Posgrado (SIP-IPN) under research grants 20071088, 20082694 and 20082887.
PY - 2008/6/16
Y1 - 2008/6/16
N2 - The identification of the unknown parameters of the Duffing's mechanical system, based on an algebraic approach, is presented. This approach is fast, accurate, and simple to numerically implement. Also, the method, combined with a suitable invariant filter, can became robust against high frequency output measurement noises. Our method uses the availability of one measurable output and produces an exact formula for the unknown parameters, which may be realized in terms of iterated convolutions. First, we show that the Duffing's system parameters are linearly identifiable with respect to the position variable, then we obtain a linear system where the unknowns are the unavailable parameters. Suitable algebraic operations on the output differential equations makes the identification schema independent of the unavailable initial conditions of the underlying nonlinear dynamical system.
AB - The identification of the unknown parameters of the Duffing's mechanical system, based on an algebraic approach, is presented. This approach is fast, accurate, and simple to numerically implement. Also, the method, combined with a suitable invariant filter, can became robust against high frequency output measurement noises. Our method uses the availability of one measurable output and produces an exact formula for the unknown parameters, which may be realized in terms of iterated convolutions. First, we show that the Duffing's system parameters are linearly identifiable with respect to the position variable, then we obtain a linear system where the unknowns are the unavailable parameters. Suitable algebraic operations on the output differential equations makes the identification schema independent of the unavailable initial conditions of the underlying nonlinear dynamical system.
KW - Chaos
KW - Duffing's mechanical system
KW - Reconstruction
UR - http://www.scopus.com/inward/record.url?scp=44449131983&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2008.04.047
DO - 10.1016/j.physleta.2008.04.047
M3 - Artículo
SN - 0375-9601
VL - 372
SP - 4569
EP - 4573
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 25
ER -