Department of Mechanical Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong.
Neural Netw. 2011 Sep;24(7):759-66. doi: 10.1016/j.neunet.2011.03.015. Epub 2011 Mar 14.
A novel H(∞) robust control approach is proposed in this study to deal with the learning problems of feedforward neural networks (FNNs). The analysis and design of a desired weight update law for the FNN is transformed into a robust controller design problem for a discrete dynamic system in terms of the estimation error. The drawbacks of some existing learning algorithms can therefore be revealed, especially for the case that the output data is fast changing with respect to the input or the output data is corrupted by noise. Based on this approach, the optimal learning parameters can be found by utilizing the linear matrix inequality (LMI) optimization techniques to achieve a predefined H(∞) "noise" attenuation level. Several existing BP-type algorithms are shown to be special cases of the new H(∞)-learning algorithm. Theoretical analysis and several examples are provided to show the advantages of the new method.
本文提出了一种新颖的 H(∞)鲁棒控制方法来解决前馈神经网络（FNN）的学习问题。通过估计误差，将 FNN 的期望权值更新律的分析和设计转化为离散动态系统的鲁棒控制器设计问题。因此，可以揭示一些现有学习算法的缺点，特别是在输入或输出数据快速变化或输出数据受到噪声污染的情况下。基于这种方法，可以利用线性矩阵不等式（LMI）优化技术找到最优的学习参数，以达到预定的 H(∞)“噪声”衰减水平。几个现有的 BP 型算法被证明是新的 H(∞)学习算法的特例。理论分析和几个例子表明了新方法的优势。
