Thiswork addresses the trajectory-tracking-control problem for a quadrotor unmanned aerial vehicle with external disturbances and parameter uncertainties. A novel adaptive-dynamic-programming-based robust control method is proposed to eliminate the effects of lumped uncertainties (including external disturbances and parameter uncertainties) and to ensure the approximate optimal control performance. Its novelty lies in that two radial basis function neural network observers with fixed-time convergence properties were first established to reconstruct the lumped uncertainties. Notably, they tune only the scalar parameters online and have low computational complexities. Subsequently, two actor–critic neural networks were designed to approximate the optimal cost functions and control policies for the nominal system. In this design, two new actor–critic neural network weight update laws are proposed to eliminate the persistent excitation condition. Then, two adaptive-dynamic-programming-based robust control laws were obtained by integrating the observer reconstruction information and the nominal control policies. The uniformly ultimately bounded stability of the closed-loop tracking control systems was ensured using the Lyapunov methodology. Finally, numerical results are shown to verify the effectiveness and superiority of the proposed control scheme.