Analysis and parameter estimation of non-linear systems via shifted Chebyshev expansions

Abstract

Abstract The expansion of the shifted Chebyshev polynomials is applied to the analysis and parameter estimation of a non-linear system represented by a Hammerstein model. By using the shifted Chebyshev expansion, a non-linear state equation is reduced to a linear algebraic matrix equation, which can be solved using a digital computer. Through the shifted Chebyshev expansion of the measured input-output data of the non-linear system, unknown parameters are estimated using the least-squares method. Illustrative examples are given to demonstrate the accuracy of this approach.