Time-varying sliding mode control for spacecraft attitude tracking maneuvers with a quadratic cost

In this paper, the problem of spacecraft attitude tracking maneuvers in the presence of parametric uncertainty and external disturbance is addressed. A time-varying sliding mode controller with an exponential time-varying sliding surface is presented. The attitude of spacecraft is represented by modified Rodrigues parameters for the non-redundancy. The proposed control algorithm eliminates the reaching phase of conventional time-invariant sliding mode control and guarantees the sliding mode occurrence all the time. This property indicates that the controller is global robust against matched parametric uncertainty and external disturbance. Additionally, the control parameter is adjusted to minimize a given quadratic cost. Finally, a numerical simulation is employed to verify the proposed control algorithm.