Minimum-fuel geostationary east-west station-keeping using a three-phase deep neural network

With the development of Electric Propulsion (EP) systems in the geostationary region, indirect optimization method shows a great potential in solving the station-keeping control law. Three main challenges, including the strong nonlinearity of the equations of motion for both states and costate, the consideration of the free-transfer-time constraint, and the Earth-shadow prediction, are hindering the autonomous control onboard. In this study, a three-phase Deep Neural Network (DNN) with three modules is proposed to achieve autonomous station-keeping by providing the optimal transfer time, the prediction of the Earth's shadow, and the initial costate guess for the East-West Station Keeping (EWSK) mission. Compared with the traditional method, the efficiency of the proposed solver is significantly increased since the minimum-fuel problem is directly solved without calculating the minimum-time solution. Numerical assessment results can indicate that the DNN could provide the parameters accurately with high scalability. Particularly, an expected success rate can be obtained to validate the autonomous EWSK strategy.