The task space control of robot manipulators requires solving the thorny problem of stabilizing the compound system {outer controller - inner controller - robot manipulator}. To stabilize this compound system, both controllers must be designed by the user to achieve convergence of the tracking error. This problem is tricky to solve in the case of the control of an industrial robot manipulator because its internal controller is not accessible to users. In this work, we propose an adaptive neural network outer controller. The neural networks approximate the dynamics of the inner controller, the kinematic and dynamic parameters of the robot. Besides, the adaptive part finds parameters that achieve the stability of the global system. Since an adaptive approach is sensitive to errors in initial values, we have integrated into the controller a term that constrains the closed-loop system to maintain the prescribed performances. The effectiveness of the approach is demonstrated through Lyapunov's theory, simulation comparisons, and experimental studies.