A Fourier Series Neural Network and Its Application to System Identification

Abstract

A distinctive neural network architecture, called the Fourier Series Neural Network (FSNN), is developed with particular consideration for applications in the area of system identification and control. This paper focuses on the theory of the FSNN and its application to system identification. This neural network is based on the topological structure of the multiple Fourier series, and is shown to be free of local minima. The global stability of the FSNN learning dynamics is guaranteed using the Delta learning rule. This paper demonstrates that the trained FSNN model approximates the Fourier series representation of an identified system with the network state weights approximating the coefficients of the Fourier series. This feature enables the FSNN to estimate the frequency spectrum of an unknown system, making the FSNN a powerful tool for controller design or on-line adaptive tuning based on system frequency response. The capabilities of the FSNN are demonstrated for linear and nonlinear systems by applying the FSNN to estimate the amplitude and phase spectrums of a second order linear transfer function and to model nonlinear inverse robot kinematics. These evaluations indicate that the FSNN modeling technique is applicable to both linear and nonlinear systems with multi-inputs and multi-outputs.