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Inverse optimal neural control for a class of discrete‐time nonlinear positive systems
Author(s) -
Leon Blanca S.,
Alanis Alma Y.,
Sanchez Edgar N.,
RuizVelazquez Eduardo,
OrnelasTellez Fernando
Publication year - 2012
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2267
Subject(s) - control theory (sociology) , nonlinear system , discrete time and continuous time , affine transformation , artificial neural network , trajectory , controller (irrigation) , mathematics , tracking error , kalman filter , computer science , optimal control , inverse , mathematical optimization , control (management) , artificial intelligence , statistics , physics , quantum mechanics , astronomy , pure mathematics , agronomy , biology , geometry
SUMMARY In this paper, a discrete‐time inverse optimal trajectory tracking for a class of nonlinear positive systems is proposed. The scheme is developed for MIMO affine discrete‐time positive nonlinear systems. This optimal controller is based on discrete time passivity and positive systems theory. The advantage of this scheme is that it avoids solving the associated Hamilton–Jacobi–Bellman equation and minimizes a meaningful cost function. The affine discrete‐time positive nonlinear system is obtained from an online neural identifier, which uses a recurrent neural network, trained with the extended Kalman filter. The applicability of the proposed approach is illustrated via simulation by trajectory tracking control of type 1 diabetes mellitus patients. Copyright © 2012 John Wiley & Sons, Ltd.