The development of autonomous unmanned aerial vehicle (UAV) spraying systems requires a mathematically rigorous control framework to ensure stability, efficiency, and robustness under uncertain field conditions. This study presents a hybrid mathematical–AI approach that integrates nonlinear optimization and control theory with adaptive machine learning for precision agriculture. The UAV path and spray scheduling problems are formulated as a constrained multi-objective optimization model that minimizes energy expenditure and chemical use while satisfying coverage and drift constraints. Using graph-theoretic modeling and nonlinear programming, optimal trajectories are derived that guarantee convergence toward feasible solutions under bounded uncertainty. Reinforcement learning is then employed to provide adaptive control, while maintaining mathematically verifiable stability through Lyapunov-based performance analysis. The proposed hybrid controller couples the learning dynamics of the AI model with the deterministic properties of the mathematical control law, ensuring predictable behavior even under varying canopy and wind conditions. Simulation experiments demonstrate significant improvements in deposition uniformity and chemical savings compared with conventional fixed-rate strategies. By grounding UAV spraying in the principles of optimization theory, stability analysis, and control mathematics, this work moves beyond heuristic AI control to a mathematically interpretable and generalizable framework. The study illustrates how integrating rigorous mathematical formulation with intelligent control design can advance sustainable and precision-driven agricultural automation.