A generalized minimal residual based iterative back propagation algorithm for polynomial nonlinear models

Abstract

In this paper, a back propagation algorithm is proposed for polynomial nonlinear models using generalized minimal residual method. This algorithm, based on Arnoldi’s method, can be regarded as a modified gradient descent iterative algorithm, and provides several advantages over the traditional gradient descent iterative algorithm: (1) has less computational efforts for systems with missing data/large-scale systems; (2) does not require the eigenvalue calculation in step-length design; (3) adaptively computes the step-length in each iteration. Therefore, it can be employed for large-scale system identification. The feasibility and effectiveness of the proposed algorithm are established in theory and demonstrated by two simulation examples.