Computer Algorithms for Pseudo-Formal Linearization Method Based on Discrete Fourier Series Expansion and Nonlinear Observer

Abstract

In this paper, we propose a computational algorithm of a pseudo-formal linearization method for nonlinear dynamic systems using the discrete Fourier series expansion in order to reduce computational burden. A nonlinear dynamic system is transformed into some augmented linear systems piecewisely with respect to a linearization function that consists of trigonometric functions by a pseudo-formal linearization method using the discrete Fourier series expansion. Then all of the linearized systems are smoothly united into a single linear system. As an application of this method, a computational algorithm for a nonlinear observer is also proposed. Numerical experiments are demonstrated to indicate the effectiveness of the proposed algorithms.