论文标题
用于回归，分类和Lyapunov控制动态系统的二次神经网络的分析和设计
Analysis and Design of Quadratic Neural Networks for Regression, Classification, and Lyapunov Control of Dynamical Systems
论文作者
论文摘要
本文介绍了最近在文献中引入的二次神经网络的分析和设计，及其在动态系统的回归，分类，系统识别和控制中的应用。这些网络提供了几个优点，其中最重要的是该架构是设计的副产品，并且不能确定a-priori，可以通过解决凸优化问题来完成他们的培训，以便实现重量的全球最佳优势，并且可以通过二次形式分析输入输出映射。从几个示例中也看出，这些网络仅使用一小部分培训数据就可以很好地工作。纸张铸造回归，分类，系统识别，稳定性和控制设计作为凸优化问题的结果，可以用多项式时间算法有效地求解到全局最佳。几个示例将显示二次神经网络在应用中的有效性。
This paper addresses the analysis and design of quadratic neural networks, which have been recently introduced in the literature, and their applications to regression, classification, system identification and control of dynamical systems. These networks offer several advantages, the most important of which are the fact that the architecture is a by-product of the design and is not determined a-priori, their training can be done by solving a convex optimization problem so that the global optimum of the weights is achieved, and the input-output mapping can be expressed analytically by a quadratic form. It also appears from several examples that these networks work extremely well using only a small fraction of the training data. The results in the paper cast regression, classification, system identification, stability and control design as convex optimization problems, which can be solved efficiently with polynomial-time algorithms to a global optimum. Several examples will show the effectiveness of quadratic neural networks in applications.
