时变环境下的新型神经网络解析建模方法及机理研究

Because of its high-speed parallel distributed nature, self-adaptation ability and convenience of hardware implementation, Recurrent neural networks are now regarded as a powerful alternative for online computation and optimization.In this project, by defining a matrix(or vector)-valued indefinite unbounded error function, a new type of neural design approach is constructed exploringly to solve exactly and efficiently the time-varying problems encountered in the engineering applications and scientific research, while the conventional gradient-based neural networks (GNN) are associated well with the time-invariant problems.Such neural network is descripted by an implicit dynamic matrix equation, which might conciede well with systems in nature and in practice. GNN is generally constructed by a scale-valued norm-based nonnegative low-bounded energy function, and thus its dyamical equation is explicit. Moreover, this new model belongs to a predictive approach because it makes good use of the time-derivative information of the time-varying coefficients. This leads to the new model could solve such time-varying problems with exactiveness and efficientiveness. In constrast, belonging to a conventional tracking approach, GNN could not catch the exact solution which is on the "move". Based on the new neural model, we maybe exploit the electronical and/or optical circuits for the online solution of the time-varying problems. This project research might provide a new computing method for the.time-varying problems appearing in the engineering and scientific fields.

递归神经网络具有潜在的高速并行性、分布式存储和自适应学习的特点，使其成为一种实时在线求解的强有力计算工具之一。针对传统基于梯度法的递归神经网络一般仅能准确有效求解定常问题的特点，本项目通过定义一种基于矩阵（或向量）取值的不定无界的误差函数，探索构造出一种能够准确有效求解在工程应用和科学研究中经常遇到的时变问题的新型神经网络设计方法。根据相关的矩阵理论分析，表明新型神经网络是用自然界中更为普遍的隐性动力学方程表述的。而梯度神经网络模型的构造则一般是基于标量范数取值的非负（或下有界）的能量函数，其动力学方程为显性。而且，由于充分利用了时变系数的导数信息，新模型具有一定的预测指导能力，故而可准确有效求解时变问题；而一般模型属于.跟踪的方法，其解仅能近似趋近理论解。在新模型结构建模的基础上，可开发出实时问题求解的电子或光学计算模块。本课题的研究或将为工程与科学领域中的时变问题提供一种新的求解思路。

递归神经网络是指在其网络结构中含有一个或多个反馈环节的神经网络，它能够实现对非线性系统真正的动态建模。因其网络结构复杂特点，存在诸如网络逼近性能不佳，稳定收敛性能不理想等问题，一般分为动态递归神经网路和静态递归神经网络。本文研究的递归神经网络是遵循张等人设计思想提出的一种新型递归神经网络算法(NRNN)，该网络算法能充分利用系数的时间导数信息，有效用于实际工程中经常遇到的时变问题解析。一般而言，传统的梯度递归神经网络(GNN)定义的是基于标量范数取值的非负的能量函数，且其仅能准确有效地求解定常的矩阵方程。与GNN相比，NRNN由于结构中的时变动态信息不仅可以准确解决时变问题，还可以描述非线性控制系统的动态特性，有效处理非线性控制系统中的跟踪控制问题。