Open AccessConstrained generalised minimum variance controller design using projection‐based recurrent neural network
Author(s) -
Toshani Hamid,
Farrokhi Mohammad,
Alipouri Yousef
Publication year - 2017
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2016.0141
Subject(s) - weighting , control theory (sociology) , projection (relational algebra) , convergence (economics) , mathematical optimization , stability (learning theory) , controller (irrigation) , artificial neural network , mathematics , minimum variance unbiased estimator , variance (accounting) , quadratic programming , computer science , projection method , dykstra's projection algorithm , control (management) , algorithm , mean squared error , artificial intelligence , statistics , business , accounting , biology , agronomy , medicine , machine learning , economics , radiology , economic growth
In this study, a generalised minimum variance control (GMVC) method using the projection‐based recurrent neural network (PRNN) is proposed to minimise the error variance in the output of the non‐linear plant. One the main drawbacks of the conventional GMVC approaches is the lack of a systematic procedure to deal with the input constraints. In this study, the PRNN is employed for incorporating the input constraints to the minimum variance index. This network is based on the optimality conditions of a constrained problem and is designed using projection theorem. To formulate the proposed approach, by considering an ARMAX model of the system and converting the cost function to a quadratic programming problem, the dynamics and output equations of the PRNN is obtained. The stability and global convergence of the PRNN is analytically shown. Moreover, suitable conditions for the weighting matrices of the cost function are determined to ensure the closed‐loop stability. The proposed control method is applied to the non‐linear quadruple tank and a comparative analysis between MVC, GMVC and the proposed approach is performed.