Various embodiments of the invention are neural network adaptive control systems and methods configured to concurrently consider both recorded and current data, so that persistent excitation is not required. A neural network adaptive control system of the present invention can specifically select and record data that has as many linearly independent elements as the dimension of the basis of the uncertainty. Using this recorded data along with current data, the neural network adaptive control system can guarantee global exponential parameter convergence in adaptive parameter estimation problems. Other embodiments of the neural network adaptive control system are also disclosed.