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A neural network-based controller is developed to enable a chaser spacecraft to approach and capture a disabled Environmental Satellite (ENVISAT). This task is conventionally tackled by framing it as an optimal control problem. However, the optimization of such a problem is computationally expensive and not suitable for onboard implementation. In this work, a learning-based approach is used to rapidly generate the control outputs of the controller based on a series of training samples. These training samples are generated by solving multiple optimal control problems with successive iterations. Then, Radial Basis Function (RBF) neural networks are designed to mimic this optimal control strategy from the generated data. Compared with a traditional controller, the neural network controller is able to generate real-time high-quality control policies by simply passing the input through the feedforward neural network. [ABSTRACT FROM AUTHOR]