An Optimal Nonlinear Regulator Design with Neural Network and Fixed Point Theorem

Dawei CAI  Yasunari SHIDAMA  Masayoshi EGUCHI  Hiroo YAMAURA  Takashi MIYAZAKI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E76-A    No.5    pp.772-776
Publication Date: 1993/05/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section LETTER (Special Section on Neural Nets,Chaos and Numerics)
Category: Neural Nets--Theory and Applications--
neural network,  nonlinearity,  optimal control,  regulator,  fixed point problem,  

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A new optimal nonlinear regulator design method is developed by applying a multi-layered neural network and a fixed point theorem for a nonlinear controlled system. Based on the calculus of variations and the fixed point theorem, an optimal control law containing a nonlinear mapping of the state can be derived. Because the neural network has not only a good learning ability but also an excellent nonlinear mapping ability, the neural network is used to represent the state nonlinear mapping after some learning operations and an optimal nonlinear regulator may be formed. Simulation demonstrates that the new nonlinear regulator is quite efficient and has a good robust performance as well.