Satellite formation keeping via real-time optimal control and iterative learning control

In this paper, we focus on the design of fuel-optimal satellite formation keeping strategy using a low thrust propulsion system. The proposed controller includes feedback control and feedforward control. For feedback control, a real-time fuel-optimal control approach is proposed. The fuel-optimal control problem is then converted into a quadratic programming problem by application of a Legendre pseudospectral method. In the optimization problem, we adopt our recently developed linear time-varying relative dynamics to accurately describe relative motion in the presence of earth oblateness effect and eccentricity effect. The control acceleration constraints are included in the optimization problem to avoid control saturation for low-thrust propulsion system. In addition, in order to meet the requirement of high-precision formation keeping for some satellite formation flying missions, a feedforward control: iterative learning control (ILC) is used for the existing close-loop feedback control system. ILC aims to improve formation keeping accuracy by eliminating the effects of periodic perturbations such as gravitational perturbation, atmospheric drag. Simulation results demonstrate the efficiency of our proposed method.