| Key Words |
Volterra series model; Wiener G-functionals; approximation of nonlinear systems; Legendre orthogonal polynomial series |
| Abstract |
This paper considers the problem of orthogonal series approximation of nonlinear systems described by Volterra series and G-functionals of Wiener. The Volterra series model is an input/output description of time-invariant nonlinear systems, where the Volterra kernels serve as generalizations for the linear system input response. Several model properties and conditions for the series convergence are presented. The Wiener G-functionals are orthogonal functions of time, where the input signal of the system is white gaussian noise. They describe nonhomogeneous input/output operators, i.e., operators where the change in the input signal level changes the level and the form of the output signal. The additional orthogonality introduced by Wiener, significantly simplifies their computation. The Volterra kernels and the Wiener G-functionals are approximated by orthogonal polynomials of Legendre. Legendre orthogonal polynomials are very effective when used for approximation of time functions on a finite interval of time. Formulas for computing the Fourier coefficients are developed. Several numerical examples for orthogonal series representation of order N = 1 for the nonlinear system with k |
| Article PDF | Download article (PDF) |
