面向时变问题求解的抗噪递归神经网络模型的设计与分析

There always exist errors or disturbances in the real-time computations, which can be deemed as noises. Existing frameworks on computation essentially lack a mechanism to directly consider noises. In contrast, the control perspective has tools, such as integral control and internal model principle to deal with noises. Solving equations bears an essential similarity with controlling dynamic systems: their residual errors are required to decrease to an acceptably small value as soon as possible. The exploitation of this similarity provides a possibility to investigate computational methods from the perspective of control theory. The shift from computation perspective to control perspective motivates us to leverage the unique control tools for performance improvement. In view of this, this project aims at investigating the model design, analysis and application of the noise-tolerant recurrent neural network from the perspective of control. Specifically, on the basis of the previous work of the applicant and his team, the following three parts of project research will be conducted: 1) designing recurrent neural network models from the perspective of control; 2) developing recurrent neural network models for time-varying optimization subject to inequality constraints; 3) developing non-convex and saturation-allowed activated functions for improving the performances of recurrent neural networks. The results of this research will not only help to solve the time-varying problems better and more effectively in the noisy environment, but also tremendously promote the engineering practice application of neural networks.

在实时计算中，各类可被视为是噪声的误差和扰动无法避免。现有的计算相关的框架本质上缺乏一种直接考虑噪声的机制。相反地，控制理论中却有不少成熟的工具，如积分控制和内模控制，用以处理这类本质为扰动的噪声。求解各类方程与控制动态系统具有一个本质上的相似性，即所对应的误差需要尽快地减小至一个较小的可接受值。这种相似性提供了一种从控制理论角度研究计算方法的手段。鉴于此，在申请者及团队之前的工作基础上，本项目将开展如下三方面的研究：1)从控制理论角度设计解读递归神经网络；2)开发用以求解带不等式约束的时变最优化问题的递归神经网络；3)开发满足非凸以及饱和限界约束的激励函数用以提高神经网络模型的性能。通过本项目的研究，不仅有助于更好、更有效地实时求解受噪声干扰的时变问题，同时还将有力地推动神经网络的工程实践应用。

实时计算领域一个不可忽视的重要问题是各类可被视为是噪声的误差和扰动对于系统稳定，精度和计算负载的影响。为了填补高效抗噪机制的空白，项目从理论分析和实际工程应用出发，在国际上率先构建求解带噪时变计算问题的统一框架，提出了一系列高效求解时变问题的智能算法，拓展其在机器人运动规划等诸多领域的应用潜力。项目从控制理论角度设计开发出可用以求解带不等式约束的时变最优化问题的递归神经网络，开发满足非凸以及饱和限界约束的激励函数用以提高神经网络模型的性能，并拓展神经网络模型在机器人规划等领域的应用。依托项目支持，项目组累计录用发表高质量的学术论文23篇，其中期刊论文19篇（中科院一区论文15篇），国际学术会议论文4篇，专利6项，软件著作权2项，以及英文学术专著2本。项目将以神经网络研究成果推动人工智能的理论技术创新，同时对整个信息社会的应用创新提供驱动力。