Identification of Discrete Nonlinear Systems via Chebyshev Polynomials and its Error Bound

Abstract

In this paper, we propose an identification method of discrete nonlinear systems using Chebyshev polynomials. A nonlinear function of a given system is assumed to be represented by a linear combination of some Chebyshev polynomials. Each coefficient of the Chebyshev polynomials is easily evaluated by the least squares method. An error bound of the identification is estimated under an assumption of measurement errors being negligible small. Numerical examples show that the accuracy of this identification for nonlinear systems is considerably well improved as the order of the Chebyshev polynomials is increased.