Rigid spacecraft robust optimal attitude stabilization under actuator misalignments

Abstract

Optimal control techniques and related robust controller extensions have been widely studied for rigid spacecraft, but these methods cannot effectively handle the attitude stabilization problem under actuator misalignments. In this paper, a robust optimal controller is proposed for the spacecraft attitude stabilization problem under actuator misalignments. It is proved that the robust attitude stabilization problem under actuator misalignments and disturbances can be reformulated into the problem of solving the Hamilton-Jacobi-Bellman (HJB) equation. However, numerically solving the HJB equation suffers from the curse of dimensionality. By proving its positive definiteness, the value function for Sontag's formula is taken as the substitute for the solution of the HJB equation to analytically construct the robust optimal controller. Thus the computational burden of implementing the controller is significantly reduced. Simulation results also demonstrate the effectiveness and efficiency of the proposed controller.