Study on maintaining formations during satellite formation flying based on SDRE and LQR

Due to the influence of various perturbations of space, satellites flying in formation cannot maintain specific configurations for long durations [1, 2]. In order to ensure that formation configurations are able to meet the requirements of space missions, it is important to maintain control of formation configurations. This is an urgent problem to be solved. The traditional control method for controlling formations is based on the average orbit element, and uses the assumption that the average orbit element deviation and the instantaneous orbit element deviation are approximately equal. However, the continuous control system is more difficult to achieve in engineering practice. Using a LQR (linear quadratic regulator) optimal control algorithm and SDRE (state-dependent Riccati equation) optimal control algorithm to maintain the formation flying [3, 4]. Through simulation, it was found that when using the SDRE controller in the system transition process time is shorter than when the LQR controller is used, and fuel consumption is less for the SDRE controller than for the LQR controller.