This paper presents the design and implementation of a reinforcement learning-based neural network controller for a differential drive mobile robot. A comprehensive mathematical model was developed, including kinematics, dynamics, and electromechanical aspects. A simulation environment was created using MATLAB/Simulink Multibody to emulate realistic robot behavior. The Deep Deterministic Policy Gradient (DDPG) algorithm was applied to train the controller, achieving effective velocity regulation and stable trajectory tracking. However, a key challenge identified was the sensitivity of the RL agent to system parameter changes, such as mass variations, which required retraining. To address this limitation, a novel hybrid controller, termed the DDPG-Augmented MRAC (DAM) controller, is proposed. By combining the adaptive capabilities of Model Reference Adaptive Control (MRAC) with the learned policy of DDPG, the DAM controller enables dynamic adaptation to parameter variations without costly retraining. Simulation results demonstrate that the DAM controller significantly improves robustness and tracking accuracy under varying system conditions, suggesting a promising direction for adaptive and resilient mobile robot control.