The feasibility of neural networks to control dynamic systems is examined. Control of a one-dimensional problem is initially investigated to develop an understanding of the structure and simulation of the neural networks. A nondimensional problem is also explored to apply a single neural network design to controlling a class of systems with a wide variety of modeling parameters. Finally, these techniques are applied to control a space vehicle to transfer, intercept, and rendezvous with another orbiting vehicle using the Clohessy-Wiltshire equations of relative motion in two dimensions. A combination of open-loop and closed-loop neural network controllers is shown to work effectively for this problem. Noise is added to the neural network inputs to demonstrate the robustness of these networks. / Ph. D.