Towards Higher-Order Zeroing Neural Networks for Calculating Quaternion Matrix Inverse with Application to Robotic Motion Tracking

Rabeh Abbassi, Houssem Jerbi, Mourad Kchaou, Theodore E. Simos (), Spyridon D. Mourtas and Vasilios N. Katsikis
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Rabeh Abbassi: Department of Electrical Engineering, College of Engineering, University of Hail, Hail 81451, Saudi Arabia
Houssem Jerbi: Department of Industrial Engineering, College of Engineering, University of Hail, Hail 81451, Saudi Arabia
Mourad Kchaou: Department of Electrical Engineering, College of Engineering, University of Hail, Hail 81451, Saudi Arabia
Theodore E. Simos: Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, West Mishref 32093, Kuwait
Spyridon D. Mourtas: Department of Economics, Mathematics-Informatics and Statistics-Econometrics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559 Athens, Greece
Vasilios N. Katsikis: Department of Economics, Mathematics-Informatics and Statistics-Econometrics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559 Athens, Greece

Mathematics, 2023, vol. 11, issue 12, 1-21

Abstract: The efficient solution of the time-varying quaternion matrix inverse (TVQ-INV) is a challenging but crucial topic due to the significance of quaternions in many disciplines, including physics, engineering, and computer science. The main goal of this research is to employ the higher-order zeroing neural network (HZNN) strategy to address the TVQ-INV problem. HZNN is a family of zeroing neural network models that correlates to the hyperpower family of iterative methods with adjustable convergence order. Particularly, three novel HZNN models are created in order to solve the TVQ-INV both directly in the quaternion domain and indirectly in the complex and real domains. The noise-handling version of these models is also presented, and the performance of these models under various types of noises is theoretically and numerically tested. The effectiveness and practicality of these models are further supported by their use in robotic motion tracking. According to the principal results, each of these six models can solve the TVQ-INV effectively, and the HZNN strategy offers a faster convergence rate than the conventional zeroing neural network strategy.

Keywords: matrix inverse; quaternion; dynamical system; hyperpower iterations; zeroing neural network; robotic motion tracking (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: View citations in EconPapers (1)

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