One of the most promising approaches to achieving fusion of the light elements, as a potential large-scale energy source for the next century, is based on the magnetic confinement of an ionised high temperature plasma. Most of the current research in magnetic confinement makes use of toroidal plasma configurations in experiments known as tokamaks. Theoretical results have predicted that the characteristics of a tokamak plasma can be made more favourable to fusion if the cross-section of the plasma is appropriately shaped. However, the accurate generation of such plasmas, and the real-time control of their position and shape, represents a demanding problem involving the simultaneous adjustment of the currents through several control coils on time scales as short as a few tens of microseconds. In this paper, we present results from the first use of neural networks for the control of the high temperature plasma in a tokamak fusion experiment. This application requires the use of fast hardware, for which we have developed a fully parallel custom implementation of a multilayer perceptron, based on a hybrid of digital and analogue techniques. Our results demonstrate that the network is indeed capable of fast plasma control in accordance with the predictions of software simulations.