Computing quaternion matrix pseudoinverse with zeroing neural networks

• Published in: AIMS mathematics Vol. 8; no. 10; pp. 22875 - 22895
• Main Authors: Kovalnogov, Vladislav N., Fedorov, Ruslan V., Demidov, Denis A., Malyoshina, Malyoshina A., Simos, Theodore E., Mourtas, Spyridon D., Katsikis, Vasilios N.
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2023
• Subjects: dynamical system; mobile object localization; moore-penrose inverse; quaternion; zeroing neural network
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.20231164

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.