Remarks on Octonion-valued Neural Networks with Application to Robot Manipulator Control

High-dimensional neural networks, in which parameters and signals are extended from the real number domain into higher-dimensional domains such as the complex numbers and quaternions, have been attracting attention recently, and applications have been successfully demonstrated. In this study, we explore a hypercomplex-valued neural network using octonions and its application to control systems. An octonion-valued neural network with a feedforward network topology is considered and is applied to the design of a control system for handling dynamic control problems of a robot manipulator. In the control system, the output of the octonion-valued neural network is used as the control input for the robot manipulator to ensure that the end-effector of the robot manipulator tracks a desired trajectory in a three-dimensional space. To validate the effectiveness of using the octonion-valued neural network, computational experiments on controlling a three-link robot manipulator using the proposed control system were conducted, with the simulation results confirming the feasibility and characteristics of this network in practical control tasks.