Finite-Time Convergent Modified Davidenko Method for Dynamic Nonlinear Equations

Yinyan Zhang, Guanggang Geng

Abstract: Neurodynamic methods, especially zeroing neural networks (ZNN), are widely used for solving nonlinear equations. Being simpler than the ZNN, the Davidenko method is efficient for static nonlinear equations. However, it has been shown that there are large lagging errors when the Davidenko method is applied to dynamic nonlinear equations (DNEs). In this brief, we address this issue by proposing a modified Davidenko method via normalization, making it suitable for solving DNEs with unknown derivatives. The proposed method converges in finite time for DNEs, regardless of additive noise. Both theoretical guarantees and numerical examples of the proposed method are provided.