Computing quaternion matrix pseudoinverse with zeroing neural networks

Vladislav N. Kovalnogov; Ruslan V. Fedorov; Denis A. Demidov; Malyoshina A. Malyoshina; Theodore E. Simos; Spyridon D. Mourtas; Vasilios N. Katsikis; Vladislav N. Kovalnogov; Ruslan V. Fedorov; Denis A. Demidov; Malyoshina A. Malyoshina; Theodore E. Simos; Spyridon D. Mourtas; Vasilios N. Katsikis

doi:10.3934/math.20231164

AIMS Mathematics

2023, Volume 8, Issue 10: 22875-22895. doi: 10.3934/math.20231164

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Computing quaternion matrix pseudoinverse with zeroing neural networks

1.
Laboratory of Interdisciplinary Problems in Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia
2.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung City 40402, Taiwan
3.
Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, West Mishref, 32093 Kuwait
4.
Data Recovery Key Laboratory of Sichun Province, Neijing Normal Univ., Neijiang 641100, China
5.
Section of Mathematics, Dept. of Civil Engineering, Democritus Univ. of Thrace, Xanthi 67100, Greece
6.
Department of Economics, Mathematics-Informatics and Statistics-Econometrics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559 Athens, Greece
7.
Laboratory "Hybrid Methods of Modelling and Optimization in Complex Systems", Siberian Federal University, Prosp. Svobodny 79, 660041 Krasnoyarsk, Russia

Received: 19 May 2023 Revised: 28 June 2023 Accepted: 11 July 2023 Published: 19 July 2023
MSC : 15A24, 65F20, 68T05

In recent years, it has become essential to compute the time-varying quaternion (TVQ) matrix Moore-Penrose inverse (MP-inverse or pseudoinverse) to solve time-varying issues in a range of disciplines, including engineering, physics and computer science. This study examines the problem of computing the TVQ matrix MP-inverse using the zeroing neural network (ZNN) approach, which is nowadays considered a cutting edge technique. As a consequence, three new ZNN models are introduced for computing the TVQ matrix MP-inverse in the literature for the first time. Particularly, one model directly employs the TVQ input matrix in the quaternion domain, while the other two models, respectively, use its complex and real representations. In four numerical simulations and a real-world application involving robotic motion tracking, the models exhibit excellent performance.
- quaternion,
- Moore-Penrose inverse,
- zeroing neural network,
- dynamical system,
- mobile object localization
Citation: Vladislav N. Kovalnogov, Ruslan V. Fedorov, Denis A. Demidov, Malyoshina A. Malyoshina, Theodore E. Simos, Spyridon D. Mourtas, Vasilios N. Katsikis. Computing quaternion matrix pseudoinverse with zeroing neural networks[J]. AIMS Mathematics, 2023, 8(10): 22875-22895. doi: 10.3934/math.20231164

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Abstract

In recent years, it has become essential to compute the time-varying quaternion (TVQ) matrix Moore-Penrose inverse (MP-inverse or pseudoinverse) to solve time-varying issues in a range of disciplines, including engineering, physics and computer science. This study examines the problem of computing the TVQ matrix MP-inverse using the zeroing neural network (ZNN) approach, which is nowadays considered a cutting edge technique. As a consequence, three new ZNN models are introduced for computing the TVQ matrix MP-inverse in the literature for the first time. Particularly, one model directly employs the TVQ input matrix in the quaternion domain, while the other two models, respectively, use its complex and real representations. In four numerical simulations and a real-world application involving robotic motion tracking, the models exhibit excellent performance.

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