设定时间收敛的分数阶复值递归神经网络的模型设计及理论研究

递归神经网络表现出强大的优化计算能力，已经被成功应用于图像处理、机器人控制、模式识别等很多领域。本项目以时变复数问题为研究对象，通过复数取值的误差函数定义，以及演化公式和激励函数的设计，提出一类分数阶复值递归神经网络模型。具体研究内容有：1)针对降噪问题，研究具有容噪功能的分数阶演化公式，并对其动力学行为进行分析；2)针对收敛时间问题，研究能够在设定时间内（与初始值无关）收敛的分数阶复值非线性激励函数，并对其动力学行为进行分析；3)针对时变复数问题的求解，提出在设定时间内收敛的容噪分数阶复值递归神经网络模型，并对其动力学行为、时间复杂度和空间复杂度等进行分析。通过本项目的研究，将为求解时变复数问题提供一种新的方法，为递归神经网络模型设计提供一种新的研究思路。

Recurrent neural networks (RNNs) have shown strong optimizing and computing capability, and have been successfully applied in many fields, such as image processing, robot control, pattern recognition and so on. Through the definition of complex-valued error function and the design of evolution formula and nonlinear activation function, this project tries to propose a fractional-order complex-valued RNN for the time-varying complex-valued problems. The main research content includes the following parts: 1) A fractional-order evolution formula with noise tolerance will be proposed for solving the noise problems, and the corresponding dynamic characteristics of this fractional-order evolution formula will be analyzed. 2) A fractional-order complex-valued nonlinear activation function which can converge in the predefined-time independently of the initial values will be proposed for the convergence time, and the corresponding dynamic characteristics of this fractional-order complex-valued activation function will be analyzed. 3) A fractional-order complex-valued RNN with predefined-time convergence and noise tolerance will be proposed, and the corresponding dynamic characteristics, the time complexity and the space complexity of this fractional-order complex-valued RNN will be also analyzed. Through this project research, a novel method will be proposed for solving the time-varying complex-valued problems, and a new research idea will be proposed for designing the models of the RNNs.