Remarks on a Quaternion-Valued Echo State Network-Based Direct Controller for Discrete-Time Non-Linear Systems

In this study, we focused on quaternion-valued echo state networks (QVESNs) in which the signals, connection weight parameters and activation functions were extended from the real-number domain to the quaternion-number domain. We also explored the potential application of these QVESNs to control systems. A design method for a direct controller was presented, in which the outputs from the QVESN trained to model the inverse dynamics of the target plant served as the control inputs to the plant for controlling non-linear dynamic systems. Computational experiments involving training and testing the QVESN-based direct controller were conducted to assess its capability in servo-level control tasks for discrete-time nonlinear plants. The simulation results demonstrate the feasibility of using QVESNs for such control tasks with sufficient accuracy and indicate their potential for controlling non-linear dynamic systems.