Abstract
In this study, a control algorithm that integrates a Deep Neural Network (DNN) adaptive control architecture with a robust disturbance rejection mechanism for the underactuated mechanical system referred to as the Futura Pendulum. The study has a hybrid learning structure that combines offline supervised pretraining of the DNN's inner layers with an online adaptation law that updates the output-layer weights in real time. The adaptive mechanism is supported by a Lyapunov-based stability analysis, which guarantees the convergence of the tracking error and the boundedness of all closed-loop signals. The impact of DNN layer size on performance was investigated using standard indices (ISE, IAE, ITSE, and ITAE). The results show that the controller achieves stable tracking with minimal chattering, even under random disturbances. Numerical simulations validate the robustness, adaptability, and improved efficiency of the proposed control method, demonstrating its potential for real-time implementation in uncertain and dynamic environments.