Combination of fractional FLANN filters for solving the Van der Pol-Duffing oscillator

Abstract

Functional link artificial neural network (FLANN) has received much attention due to its wide applicability. The Van der Pol-Duffing oscillator (VdPDO)-based nonlinear systems, which own complex dynamical behaviors, identification of such nonlinear model is vital. This paper exploits the nonlocality of fractional calculus, aiming to enhance the identification accuracy of the VdPDO-based nonlinear systems. The proposed combined FEM-LMS (CFEM-LMS) algorithm, which is based on the FLANN structure, convexly combines the least mean square (LMS) algorithm and the newly proposed fractional-order error modified LMS (FEM-LMS) algorithm. The CFEM-LMS algorithm has improved performance and can dynamically adapt to the nonlinearity of the system. As an added contribution, a novel mixing parameter adaptation criterion is proposed for performance improvement. Extensive simulation results in the context of VdPDO-based nonlinear system identification demonstrate the superiority of the proposed algorithm as compare to state-of-the-art approaches.