Finite-time stability control of the Sun-Earth heliostationary flight

In this paper, we study the stabilizing control problem of the inertia hovering orbit in the restricted three body problem. In several deep space exploration, the L1 point shows many advantages. However, an active control is needed to stabilize the spacecraft. To solve this problem, this paper proposes a global robust finite time sliding mode control strategy. Based on the nonsingular terminal sliding mode control, a time-varying sliding mode control law is designed such that the tracking error converges to zero in finite time and remains zero from then on. The advantages are multi-fold: (1) the error convergence time can be given in advance; (2) the convergence rate can be adjusted by changing a specific parameter of the controller; (3) the system can always stay on the sliding surface from the initial moment, which indicates that the controller has global sliding characteristics. Finally, numerical simulations are implemented to verify the method.