Identification by Chebyshev polynomials for discrete noisy nonlinear systems

We propose an identification method of discrete noisy nonlinear systems using Chebyshev polynomials. The nonlinear function is represented by the 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 also estimated. Also the optimal order of the Chebyshev polynomials is determined by using Akaike's information criterion. Numerical examples demonstrate that the accuracy of this identification for nonlinear systems is considerably improved.