On the algebraic reconstruction of the Duffing's mechanical system

Carlos Aguilar-Ibanez, Jorge H. Sanchez H., Miguel S.C. Suárez C., Juan Martinez C.

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)4569-4573
Number of pages5
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume372
Issue number25
DOIs
StatePublished - 16 Jun 2008

Keywords

  • Chaos
  • Duffing's mechanical system
  • Reconstruction

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