Global Stability and Robustness Properties of Neural Control Systems

在过去的十年里，神经网络在工程系统的识别和控制中的使用一直是激烈的辩论。尽管关于神经网络在辨识和控制中的稳定性的文献中已经得到了一些结果，但这些结果大多是局部的和/或包含相当严格的条件，在这些条件下稳定性是有效的。与这些分析结果相反，实际应用和数值模拟的结果恰恰相反：神经网络确实是强大的数值计算单元，能够很好地逼近非线性映射，并在很大范围内提供估计、控制和优化的复杂功能。该项目的目标是解决这一差距，并开发能够解释神经网络在用于非线性控制时的真实运行范围的全局稳定性工具。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著特征，并推导出潜在的收敛和稳定性性质。文献[1]中的初步结果表明，在使用神经网络的辨识问题中，有可能得到全局收敛的条件。P.I.计划推出训练算法，以及在哪些条件下可以得出使用神经网络的全局系统辨识以及使用神经控制器的全局稳定性。我们将研究各种神经网络结构，包括多层感知器和径向基函数。我们将研究类梯度算法在这些问题中的适用性和局限性。所有的理论推导都将得到模拟研究的补充。拟议的研究结果将在各种工程问题中的复杂动态系统的分析和设计方面带来根本性的进步。

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.***