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A Qualitative Study of Time-Lagged Recurrent Networks

时滞循环网络的定性研究

基本信息

批准号：
9732785
负责人：
Derong Liu
金额：
$ 11.63万
依托单位：
Stevens Institute of Technology
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
1998
资助国家：
美国
起止时间：
1998-09-01 至 2000-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9732785&HistoricalAwards=false
关键词：
Qualitative Study Time Lagged Recurrent

项目摘要

ECS-9732785LiuTime-Lagged Recurrent Networks (TLRN)are known to be more powerful than feedforward multilayer neural networks and in nonlinear systems identification and control. This project will investigate several fundamentally important theoretical and practical questions concerning TLRN's in two areas:Structural adaptivity and robustness analysis: For nonlinear functionapproximation using neural networks, the behavior of time-laggedrecurrent networks will be studied in comparison to feedforward neural networks. It will be shown that, due to the existence of recurrencies in the network,time-lagged recurrent networks will exhibit behavior equivalent tomultilayer feedforward neural networks with time-varying parameters. It isexpected that a multilayer feedforward neural network with time-varyingpaxameters will exhibit adaptive behavior; and the study will show that time-lagged recurrent networks with fixed parameters will generally exhibit adaptivebehavior. A thorough study of how time-lagged recurrent networks willperform under parameter perturbations will also be conducted. Resultswill be given as bounds for permissible parameter perturbations whichguarantee to retain the desired performance of the network.Training based on energy function approach: Stability of recurrentNeural networks which can be translated into convergent behavior and boundedsignals and parameters in the network is of fundamental interest. Thestability properties of tiine-lagged recurrent networks will be studiedusing the Lyapunov's second method. In applying the Lyapunov second method, oneneeds to construct a Lyapunov function (or energy function). Stability isguaranteed by the fart that the Lyapunov function is positive definite andis (monotonically) decreasing over time. This stability analysis result willshed new lights on the training of neural networks for systems identification,which will lead to training algorithms with guaranteed convergence to the globalminimum or to a solution.

ECS-9732785Liu 已知时滞循环网络 (TLRN) 在非线性系统识别和控制方面比前馈多层神经网络更强大。该项目将在两个领域研究有关 TLRN 的几个基本重要的理论和实践问题：结构适应性和鲁棒性分析：对于使用神经网络的非线性函数逼近，将研究时滞循环网络的行为，并将其与前馈神经网络进行比较。结果表明，由于网络中存在循环，时滞循环网络将表现出与具有时变参数的多层前馈神经网络等效的行为。预计具有时变参数的多层前馈神经网络将表现出自适应行为；该研究将表明，具有固定参数的时滞循环网络通常会表现出自适应行为。还将对时滞循环网络在参数扰动下的表现进行深入研究。结果将作为允许的参数扰动的界限给出，以保证保留网络的所需性能。基于能量函数方法的训练：可以转化为收敛行为以及网络中的有界信号和参数的循环神经网络的稳定性具有根本意义。 Thestability properties of tiine-lagged recurrent networks will be studiedusing the Lyapunov's second method. 在应用李亚普诺夫第二方法时，需要构造一个李亚普诺夫函数（或能量函数）。 Lyapunov 函数是正定的，并且随着时间的推移（单调）递减，这保证了稳定性。这一稳定性分析结果将为用于系统识别的神经网络训练提供新的思路，这将导致训练算法保证收敛到全局最小值或解决方案。