This paper proposes a framework for robust design of UAV-assisted wireless networks that combine 3D trajectory optimization with user mobility prediction to address dynamic resource allocation challenges. We proposed a sparse second-order prediction model for real-time user tracking coupled with heuristic user clustering to balance service quality and computational complexity. The joint optimization problem is formulated to maximize the minimum rate. It is then decomposed into user association, 3D trajectory design, and resource allocation subproblems, which are solved iteratively via successive convex approximation (SCA). Extensive simulations demonstrate: (1) near-optimal performance with $\epsilon \approx 0.67\%$ deviation from upper-bound solutions, (2) $16\%$ higher minimum rates for distant users compared to non-predictive 3D designs, and (3) $10-30\%$ faster outage mitigation than time-division benchmarks. The framework's adaptive speed control enables precise mobile user tracking while maintaining energy efficiency under constrained flight time. Results demonstrate superior robustness in edge-coverage scenarios, making it particularly suitable for $5G/6G$ networks.