Global Stability and Robustness Properties of Neural Control Systems

神经控制系统的全局稳定性和鲁棒性

• 批准号: 0070039
• 负责人: Anuradha Annaswamy
• 金额: $ 22.28万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-06-15 至 2003-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0070039&HistoricalAwards=false
• 关键词: Global; Stability; Robustness; Properties; Neural

0070039AnnaswamyThe use of neural networks in identification and control of engineering systems has been intensely debated over the past decade. Despite the fact that several stability results have been derived in the literature concerning neural networks in identification and control, most of them are local in nature and/or include fairly restrictive conditions under which the stability is valid. In contrast to these analytical results, the actual demonstration in applications and numerical simulations reports just the contrary: Neural networks indeed serve as powerful numerical computational units that are capable of very good approximations of nonlinear maps and provide complex functionalities of estimation, control, and optimization over a large region of operation. The goal of this project is to address this gap and develop global stability tools that are capable of explaining the true scope of operation of a neural network when used for nonlinear control. The main idea here is to directly address and exploit the distinguishing feature of nonlinear regression in neural networks and derive the underlying convergence and stability properties. Preliminary results in [I] show that it is possible to derive conditions under which global convergence takes place in identification problems using neural networks. The P.I. plans to derive training algorithms as well as conditions under which global system identification using neural networks as well as global stability using neural controllers can be derived. Various neural network structures including multi-layered perceptrons and radial basis functions will be examined. The applicability as well as limitations of gradient-like algorithms in these problems will be studied. All theoretical derivations will be complemented by simulation studies. The results from the proposed research will lead to fundamental advances in the analysis and design of complex dynamic systems in various engineering problems.***

0070039 Annaswamy在过去的十年里，神经网络在工程系统的识别和控制中的应用一直受到激烈的争论。 尽管在有关神经网络识别和控制的文献中已经得到了一些稳定性结果，但大多数结果都是局部的，并且/或者包括相当严格的条件，在这些条件下稳定性是有效的。 与这些分析结果相反，应用和数值模拟中的实际演示报告恰恰相反：神经网络确实是强大的数值计算单元，能够很好地近似非线性映射，并在大范围内提供复杂的估计，控制和优化功能。该项目的目标是解决这一差距，并开发全局稳定性工具，能够解释神经网络用于非线性控制时的真实操作范围。 这里的主要思想是直接处理和利用神经网络中非线性回归的显着特征，并推导出基本的收敛性和稳定性。文[1]的初步结果表明，在用神经网络进行辨识时，可以导出全局收敛的条件。 私家侦探导出训练算法的计划以及可以导出使用神经网络的全局系统识别以及使用神经控制器的全局稳定性的条件。 各种神经网络结构，包括多层感知器和径向基函数将被检查。 将研究类梯度算法在这些问题中的适用性和局限性。 所有理论推导都将通过模拟研究来补充。 从拟议的研究结果将导致在各种工程问题的复杂动态系统的分析和设计的根本性进展。