Hermitian Solutions of the Quaternion Algebraic Riccati Equations through Zeroing Neural Networks with Application to Quadrotor Control

Houssem Jerbi, Obaid Alshammari, Sondess Ben Aoun, Mourad Kchaou, Theodore E. Simos (), Spyridon D. Mourtas and Vasilios N. Katsikis
Additional contact information
Houssem Jerbi: Department of Industrial Engineering, College of Engineering, University of Hail, Háil 81481, Saudi Arabia
Obaid Alshammari: Department of Electrical Engineering, College of Engineering, University of Hail, Háil 81481, Saudi Arabia
Sondess Ben Aoun: Department of Computer Engineering, College of Computer Science and Engineering, University of Hail, Háil 81451, Saudi Arabia
Mourad Kchaou: Department of Electrical Engineering, College of Engineering, University of Hail, Háil 81481, Saudi Arabia
Theodore E. Simos: Laboratory of Interdisciplinary Problems of Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia
Spyridon D. Mourtas: Department of Economics, Mathematics-Informatics and Statistics-Econometrics, National and Kapodistrian University of Athens, 10559 Athens, Greece
Vasilios N. Katsikis: Department of Economics, Mathematics-Informatics and Statistics-Econometrics, National and Kapodistrian University of Athens, 10559 Athens, Greece

Mathematics, 2023, vol. 12, issue 1, 1-19

Abstract: The stability of nonlinear systems in the control domain has been extensively studied using different versions of the algebraic Riccati equation (ARE). This leads to the focus of this work: the search for the time-varying quaternion ARE (TQARE) Hermitian solution. The zeroing neural network (ZNN) method, which has shown significant success at solving time-varying problems, is used to do this. We present a novel ZNN model called ’ZQ-ARE’ that effectively solves the TQARE by finding only Hermitian solutions. The model works quite effectively, as demonstrated by one application to quadrotor control and three simulation tests. Specifically, in three simulation tests, the ZQ-ARE model finds the TQARE Hermitian solution under various initial conditions, and we also demonstrate that the convergence rate of the solution can be adjusted. Furthermore, we show that adapting the ZQ-ARE solution to the state-dependent Riccati equation (SDRE) technique stabilizes a quadrotor’s flight control system faster than the traditional differential-algebraic Riccati equation solution.

Keywords: zeroing neural network; quaternion; algebraic Riccati equation; quadrotor control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/1/15/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/1/15/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2023:i:1:p:15-:d:1304270

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().