Utilizing the well-established Dynamic Inversion(DI) theory and augmenting it with online trained neural networks in the philosophy of `modified state observer', a robust nonlinear controller catering to the actual plant model is presented in this paper. The neural network (NN) is used to capture the unmodelled dynamics due to uncertainty in the eccentricity, uncertain semi-major axis of the chief satellite and also slowly-varying external disturbance term. Neural network is trained online using `closed form expressions' and do not require any iterative process. The overall structure leads to robust control synthesis and works well despite the presence of unmodelled dynamics. This technique is applied to the challenging problem of satellite formation flying. Simulation studies show that the presented control synthesis approach is able to ensure close formation flying catering for large initial separation, high eccentricity orbits, uncertain semi-major axis of chief satellite and J2 gravitational effects, which is usually considered as an exogenous perturbation.