A Novel Approach Solving for Linear Matrix Inequalities Using Neural Networks

摘要

Linear matrix inequalities (LMIs) play avery important role in postmodern control by providinga framework that unifies many concepts. While numerouspapers have appeared cataloging applications of LMIsto control system analysis and design, there have beenfew publications in the literature describing thenumerical solution of these problems. Specially, neural network processing has rarely been used to solve those problems.This paper attempts topropose a new approach to solving a class of LMIsusing recurrent neural networks. The nature ofparallel and distributed processing renders thesenetworks, which possess the computational advantages overthe traditional sequential algorithms in real-timeapplications. The proposed networks are proven to be largelyasymptotical and capable of solving LMIs.Some illustrative examples are provided todemonstrate the proposed results.