Attitude control of rigid spacecraft with disturbance generated by time varying exosystems

• A new matrix product is applied to deal with attitude control problem.
• Internal model is introduced to handle the disturbance rejection.
• The semi-tensor product and backstepping are combined to construct the control law.

This paper is concerned with the problem of attitude control and disturbance rejection of rigid spacecraft in the presence of parameter uncertainty. It is assumed that the external disturbance is generated by some time varying exosystems. The unit quaternion is used as the kinematic variables since it is free of singularity. An internal model and an adaptive control law are proposed. The parameter uncertainty caused by the unknown inertia matrix is handled by combining the semi-tensor product and adaptive control method. The asymptotical stability of the closed-loop system is given via backstepping and Lyapunov analysis. Finally, an illustrative example is provided to show the effectiveness of the proposed approach.