Identification by Chebyshev Interpolation and its Error Bound for a Discrete-Type Nonlinear System with Measurement Noise

Abstract

In this paper, we propose an identification method of discrete-type nonlinear systems with additive measurement noises using Chebyshev polynomials. A nonlinear function is assumed to be approximately described by a linear combination of some Chebyshev polynomials. Each coefficient of the polynomials is easily evaluated by the least squares method. An error bound of the identification is also estimated here. Moreover, the optimal order of the Chebyshev polynomials is determined by using the Akaike's information criterion. The paper includes simulation experiments to demonstrate the effectiveness of the proposed method.