Chebyshev Functional Link Spline Neural Filter for Nonlinear Dynamic System Identification
Zhao Zhang, Jiashu Zhang
Abstract
In order to increase the nonlinear fitting performance of functional link neural network (FLNN), a novel chebyshev functional link spline neural filter (CFLSNF) to apply in system identification is proposed. Compared with the weak nonlinearity and boundedness of the fixed activation function (e.g., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$sigmoid$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$tanh$ </tex-math></inline-formula> ), CFLSNF has stronger nonlinear approximation ability than FLNN due to the flexible interpolation ability of spline activation function. At the same time, the proposed CFLSNF eliminates the hidden layers by using Chebyshev polynomial to extend the input space into high dimensions, which shows certain computational advantages compared with the artificial neural network (ANN) structures. Moreover, to update the weights of the CFLSNF, the CFLSNF-LMS is also developed. The stability conditions and computational complexity are studied. Besides, in order to make CFLSNF structure suitable for impulsive noise interference environment, a robust algorithm based on maximum versoria criterion is also proposed. Finally, the validity of the proposed architecture and algorithm are verified by experiments.