Solving quaternion nonsymmetric algebraic Riccati equations through zeroing neural networks-Reference-Cited by-同舟云学术

Solving quaternion nonsymmetric algebraic Riccati equations through zeroing neural networks

Published:2024 Issue:3 Volume:9 Page:5794-5809
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Jerbi Houssem¹,Al-Darraji Izzat²,Albadran Saleh³,Aoun Sondess Ben⁴,Simos Theodore E.⁵⁶⁷⁸⁹,Mourtas Spyridon D.¹⁰¹¹,Katsikis Vasilios N.¹⁰

Affiliation:

1. Department of Industrial Engineering, College of Engineering, University of Hail, Ha'il 81481, Saudi Arabia

2. Al-Khwarizmi College of Engineering, University of Baghdad, Baghdad 10081, Iraq

3. Department of Electrical Engineering, College of Engineering, University of Hail, Ha'il 81481, Saudi Arabia

4. Department of Computer Engineering, College of Computer Science and Engineering, University of Hail, Ha'il 81451, Saudi Arabia

5. Center for Applied Math. and Bioinformatics, Gulf Univ. for Science and Technology, West Mishref 32093, Kuwait

6. Department of Medical Research, China Medical Univ. Hospital, China Medical Univ., Taichung City 40402, Taiwan

7. Laboratory of Inter-Disciplinary Problems in Energy Production, Ulyanovsk State Technical Univ., 32 Severny Venetz Street, 432027 Ulyanovsk, Russia

8. Data Recovery Key Laboratory of Sichun Province, Neijing Normal Univ., Neijiang 641100, China

9. Section of Mathematics, Dept. of Civil Engineering, Democritus Univ. of Thrace, Xanthi 67100, Greece

10. Department of Economics, Division of Mathematics-Informatics and Statistics-Econometrics, National and Kapodistrian Univ. of Athens, Sofokleous 1 Street, 10559 Athens, Greece

11. Laboratory "Hybrid Methods of Modelling and Optimization in Complex Systems", Siberian Federal Univ., Prosp. Svobodny 79, 660041 Krasnoyarsk, Russia

Abstract

<abstract><p>Many variations of the algebraic Riccati equation (ARE) have been used to study nonlinear system stability in the control domain in great detail. Taking the quaternion nonsymmetric ARE (QNARE) as a generalized version of ARE, the time-varying QNARE (TQNARE) is introduced. This brings us to the main objective of this work: finding the TQNARE solution. The zeroing neural network (ZNN) technique, which has demonstrated a high degree of effectiveness in handling time-varying problems, is used to do this. Specifically, the TQNARE can be solved using the high order ZNN (HZNN) design, which is a member of the family of ZNN models that correlate to hyperpower iterative techniques. As a result, a novel HZNN model, called HZ-QNARE, is presented for solving the TQNARE. The model functions fairly well, as demonstrated by two simulation tests. Additionally, the results demonstrated that, while both approaches function remarkably well, the HZNN architecture works better than the ZNN architecture.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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