Remarks on Direct Controller using a Commutative Quaternion Neural Network

Abstract

In this study, we investigated the capability of a high-dimensional neural network (NN) using commutative quaternion numbers in control system applications. A multilayer commutative quaternion NN was employed to develop a servo-level controller, where the network input comprised the reference output and tapped-delay inputs/outputs of the object plant, and the network output was used directly as the control input. The commutative quaternion NN in the controller was trained in an offline manner using the stochastic gradient descent method to obtain the inverse transfer function of the plant. The effectiveness of the proposed controller was evaluated in computational experiments to control a discrete-time nonlinear plant. The simulation results demonstrate the feasibility of the commutative quaternion NN for this task and the characteristics of the proposed controller.