Asymptotic Reconstruction of the Fourier Expansion of an External Periodic Force
Keywords:
Identification, Li´enard oscillator, Fourier series, external perturbation, invariant relations.Abstract
The problem under consideration involves identifying the coefficients of a partial sum of a Fourier series used to approximate the effect of an external periodic force on a Li\'{e}nard oscillator. A method for constructing a nonlinear identifier is proposed, enabling the real-time asymptotical estimation of the oscillator velocity and coefficients of a partial sum of a Fourier series by means of displacement measurements. This method is based on the synthesis of invariant relations that make it possible to interrelate the variables of a special extended dynamic system and determine unknown variables as functions of known ones. The asymptotic convergence of estimates of unknowns to their true values is proven. ...
doi: https://doi.org/10.55787/jtams.2026.1.AI00137
