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Neural Networks For Matrix Scaling And S‐Procedure Problem Solving
Author(s) -
Lin ChunLiang
Publication year - 2001
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1111/j.1934-6093.2001.tb00069.x
Subject(s) - scaling , artificial neural network , norm (philosophy) , computer science , nonlinear system , matrix (chemical analysis) , stability (learning theory) , mathematical optimization , control (management) , mathematics , artificial intelligence , machine learning , physics , geometry , materials science , quantum mechanics , political science , law , composite material
Linear matrix inequalities (LMIs) play a very important role in postmodern control by providing a framework that unifies many concepts. While many papers have addressed the issue for solving LMIs using sequentially numerical algorithms, few have examined solving related LMIs using neural network processing. The aim of this paper is to show the potential of using recurrent neural networks to solve these problems. Two representative LMI problems are considered. First, the problem of scaling a matrix to reduce its norm, which appears often in robust control applications, is considered. Second, the approach is extended to solve the S‐procedure problem, which is closely related to the stability of particular nonlinear systems. Illustrative examples are provided to demonstrate use of the proposed approach.