A GOBF-wavelet wiener model for identification of nonlinear dynamic systems

Since orthogonal representations of functions are among the most desirable and efficient approximation schemes, this paper proposes an appropriate combination of two classes of orthonormal basis functions for nonlinear dynamic system identification. For this purpose, the nonlinear Wiener model is studied which consists of a linear time invariant (LTI) subsystem followed by a nonlinear static function. To describe the linear part, Generalized Orthonormal Basis Functions (GOBFs) are invoked. These orthonormal bases include the familiar Laguerre, FIR, two-parameter Kautz and Hambo bases as special cases. The nonlinear static part is approximated based on orthogonal wavelets with compact support. By appropriate combination of these two parts, a linear-in-the-parameter model is obtained. Therefore, parameter estimation is simplified to an ordinary least squares problem. Two nonlinear dynamic case studies, a simulated fermentation process and a real singlelink flexible manipulator system, are also provided which demonstrate the effectiveness of the proposed algorithm with satisfactory performance.