Summary This paper studies the output feedback tracking control problem for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics using a prescribed performance adaptive neural dynamic surface control design approach. A nonlinear mapping technique is employed to address the state constraints. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. The unmodeled dynamics is addressed by introducing an available dynamic signal. Subsequently, we construct the controller and parameter adaptive laws using a backstepping technique. Based on Lyapunov stability theory, it is shown that all signals in the closed‐loop system are semiglobally uniformly ultimately bounded and that the tracking error always remains within the prescribed performance bound. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.