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.

本文针对多项式非线性模型提出了一种基于广义最小残差法的反向传播算法。该算法基于Arnoldi的方法，可以看作是一种改进的梯度下降迭代算法，与传统的梯度下降迭代算法相比，具有以下几个优点：（1）对于缺失数据的系统/大规模系统计算量少；(2) 步长设计中不需要计算特征值；(3) 在每次迭代中自适应地计算步长。因此，它可以用于大规模系统识别。从理论上建立了所提出算法的可行性和有效性，并通过两个仿真实例进行了验证。