The shifted Legend re approach to non-linear system analysis and identification

Abstract

Applications of the shifted Legendre polynomial expansion to the analysis and identification of the non-linear system described by a Hammerstein model which consists of a single-valued non-linearity followed by a linear plant are studied. For the analysis, by using the shifted Legendre polynomial expansion, the solution of a non-linear state equation is reduced to the solution of a linear algebraic matrix equation. For the identification, through the shifted Legendre expansions of the measured input-output data, the unknown parameters of both the linear plant and the characterization of the non-linear element are estimated using the least-squares method. Algorithms are presented. Numerical examples are given to illustrate the use of this approach.