ABSTRACT

Solving nonlinear equations is a crucial step in the territories of science and engineering, as many practical problems could be mathematically described by nonlinear equations. In this paper, a novel robust fast convergence zeroing neural network (RFCZNN) by utilizing a reconstructed activation function (AF) is presented and investigated for the dynamic nonlinear equations (DNE) solving problems in predictable period. Comparing with recently reported finite-time nonlinear recurrent neural network, the presented RFCZNN solves the DNE in settled theoretical time and possesses better robustness in noise-polluted environments. Unlike the finite-time convergent neural network models, the time consumption of the presented RFCZNN in convergence process can be calculated directly by mathematics without considering modelling initial states. The comparative experimental results for solving high-order (second and third order) DNE and tracking robotic motional trail are presented separately to further represent that the proposed fixed-time convergent RFCZNN model is more robust and efficient.

摘要

求解非线性方程是科学和工程领域的关键一步，因为许多实际问题可以用非线性方程进行数学描述。在本文中，提出并研究了一种利用重构激活函数 (AF) 的新型鲁棒快速收敛归零神经网络 (RFCZNN)，用于解决可预测周期内的动态非线性方程 (DNE) 问题。与最近报道的有限时间非线性递归神经网络相比，所提出的 RFCZNN 在稳定的理论时间内解决了 DNE，并且在噪声污染环境中具有更好的鲁棒性。与有限时间收敛神经网络模型不同，本文提出的 RFCZNN 在收敛过程中的时间消耗可以直接通过数学计算，而无需考虑建模初始状态。