Remarks on Quaternion Multi-Layer Neural Network Based on the Generalised HR Calculus

This study investigates a training method of a quaternion multi-layer neural network based on a gradient-descent method extended to quaternion numbers. The gradient of the cost function is calculated using the generalised HR calculus to derive the training rule for the network parameters. Computational experiments for identifying and controlling a discrete-time nonlinear plant were conducted to evaluate the proposed method. The results confirmed the feasibility of using the GHR calculus in the quaternion neural network and showed the capability of using the quaternion neural network for a control system application.