Identification of one class of distributed parameter systems based on Chebyshev polynomials

In this paper, we studied the identification issue of one class of distributed parameter systems based on the Chebyshev polynomials. The proposed method translates distributed parameter systems into lumped parameter systems by casting state functions into the space spanned by Chebyshev polynomials, and identification can be made with the algorithm of least square parameter estimation. There is no approximation in dealing with boundary conditions, and high accuracy can be achieved by few polynomials. Numerical example is conducted to demonstrate the validity and accuracy of the proposed method.