A Study for Solving Linear Matrix Inequalities and Related Problems Using Neural Networks

• Main Authors: Teng-Hsien Huang, 黃登獻
• Other Authors: Chun-Liang Lin
• Format: Others
• Language: en_US
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/91883029949977184759

碩士 === 逢甲大學 === 自動控制工程學系 === 87 === Linear matrix inequalities (LMIs) play a very important role in postmodern control by providing a framework that unifies many concepts. While numerous papers have appeared cataloging applications of LMIs to control system analysis and design, there have been few publications in the literature describing the numerical solution to these problems. Specially, it was rarely seen that solving these problems based on neural network processing. This paper attempts to propose a new approach solving for a class of LMIs using recurrent neural networks. This approach includes three sets of recurrent neural networks each with two feedback connective layers. The gradient descent algorithm is used as the learning rule for training the neural network. In addition, the paper also presents a realization of electronic neural network for solving Lyapunov matrix equation. An algebraic derivation for converting Lyapunov matrix equations into simultaneous linear matrix equations is presented. A circuit schematic for realizing the neural networks is also designed. The nature of parallel and distributed processing renders these networks possessing the computational advantages over the traditional sequential algorithms in real-time applications. The proposed networks are proven to be asymptotically in the large and capable of LMIs and Lyapunov matrix equations solving. Some illustrative examples are provided to demonstrate the proposed results and the operating characteristics of an op-amp based neural network.