In this work we develop an Artificial Neural Network (ANN) for the feedback stabilization of a thermonuclear reactor at nearly ignited burn conditions. A volume-averaged zero dimensional nonlinear model is used to represent the time evolution of the electron density, the relative density of alpha particles and the temperature of the plasma, where a particular scaling law for the energy confinement time previously used by other authors, was adopted. The control actions include the concurrent modulation of the D-T refueling rate, the injections of a neutral He-4 beam and an auxiliary heating power modulation, which are constrained to take values within maximum and minimum levels. For this purpose a feedforward multilayer artificial neural network with sigmoidal activation function is trained using a Backpropagation Through Time technique. Numerical examples are used to illustrate the behavior of the resulting ANN-dynamical system configuration. It is concluded that the resulting ANN can successfully stabilize the nonlinear model of the thermonuclear reactor at nearly ignited conditions for temperature and density departures significatively far away from their nominal operating values. The NN-dynamical system configuration is shown to be robust with respect to the thermalization time of the alpha particles for perturbations within the region used to train the NN.