<p>This paper presents a novel hybrid control framework that incorporates nonlinear control theory with deep learning. This framework enables robust and time-efficient multi-waypoint navigation using a differential drive wheeled mobile robot (DDWMR) involving sequential halts at specific points for environment mapping purposes. It integrates a Lyapunov-based Nonlinear Position Controller (NPC) with a neural network-based parameter estimator. This combination allows real-time adaptive tuning of control gains to optimize robot behavior across dynamically evolving target configurations. A rigorous multi-objective performance metric is formulated to evaluate: line-segment adherence, arrival heading angle precision, and elapsed time. The control parameter space is explored using brute-force search to generate training data, and a multilayer perceptron is trained to generalize optimal control signals for unseen reference points within a defined workspace. Comparative simulations are conducted with a classical PID controller as well as fixed-parameter Lyapunov controller. The proposed Predictive Neural Network (PNN) method outperforms both baseline approaches. PNN consistently achieves better trade-offs across all defined control objectives. It demonstrates marked improvements in system stability and enhanced generalization to previously unseen target configurations. The method proves effective performance during sequential halts required for camera-based environmental mapping. This approach establishes a significant step toward practical, intelligent robot autonomy in constrained indoor environments.</p>