用于线性矩阵不等式问题的神经网络。

A neural network for linear matrix inequality problems.

作者信息

Lin C L, Lai C C, Huang T H

机构信息

Department of Automatic Control Engineering, Feng Chia University, Taichung, Taiwan, 40724 R.O.C.

出版信息

IEEE Trans Neural Netw. 2000;11(5):1078-92. doi: 10.1109/72.870041.

DOI:10.1109/72.870041

PMID:18249836

Abstract

Gradient-type Hopfield networks have been widely used in optimization problems solving. This paper presents a novel application by developing a matrix oriented gradient approach to solve a class of linear matrix inequalities (LMIs), which are commonly encountered in the robust control system analysis and design. The solution process is parallel and distributed in neural computation. The proposed networks are proven to be stable in the large. Representative LMIs such as generalized Lyapunov matrix inequalities, simultaneous Lyapunov matrix inequalities, and algebraic Riccati matrix inequalities are considered. Several examples are provided to demonstrate the proposed results. To verify the proposed control scheme in real-time applications, a high-speed digital signal processor is used to emulate the neural-net-based control scheme.

摘要

梯度型霍普菲尔德网络已广泛应用于优化问题求解。本文通过开发一种面向矩阵的梯度方法来解决一类线性矩阵不等式（LMI），提出了一种新颖的应用，这类不等式在鲁棒控制系统分析与设计中经常遇到。求解过程在神经计算中是并行且分布式的。所提出的网络被证明是全局稳定的。考虑了代表性的线性矩阵不等式，如广义李雅普诺夫矩阵不等式、同时李雅普诺夫矩阵不等式和代数黎卡提矩阵不等式。提供了几个例子来证明所提出的结果。为了在实时应用中验证所提出的控制方案，使用了高速数字信号处理器来模拟基于神经网络的控制方案。