Owing to their rapidly increasingapplicationsin aerospace,service,and other fields,manipulators are an area of active in-depth research.In comparison with the rigid manipulator,the flexible manipulator is light,flexible,and highly efficient.It also consumes less energy.The advantages of the flexible manipulator have made it a subject of in-depth study and further research.However,because of the particularity of the structure and build material,the operation of the flexible manipulator produces elastic deformation and vibration,which make the positioning and tracking of the manipulator difficult.Thus,it is important to study vibration suppression.In this paper,the assumed mode method is used to model the single-link flexible manipulator system andthe Lyapunov direct method is used to realize the stability of the closed-loop system.Giventhe particular constrained targets in practical use,the tangent-function form of the Lyapunov strategy is utilized to deal with the output constraints.The neural network control method is used to approach the uncertainty of the system,and the stability of the closed-loop system is analyzed by the Lyapunov method.The control performance of the controller is verified through simulations in MATLAB and experiments using the Quanser platform.