Abstract-This paper studies high-order sliding mode control laws to deal with some spacecraft attitude tracking problems. Second and third order quasi-continuous sliding control are applied to quaternion-based spacecraft attitude tracking manoeuvres. A class of linear sliding manifolds is selected as a function of angular velocities and quaternion errors. The second method of Lyapunov theory is used to show that tracking is achieved globally. An example of multiaxial attitude tracking manoeuvres is presented and simulation results are included to verify and compare the usefulness of the various controllers. I. INTRODUCTIONIn general spacecraft motion is governed by the so-called kinematics equations and dynamics equations [1]. These mathematical descriptions are highly nonlinear and thus linear feedback control techniques are not suitable for the global controller design.First-order sliding mode control has been considered as a useful scheme for spacecraft attitude control. Vadeli [2] designed a variable structure attitude control law based on quaternion kinematics. A similar approach was later proposed in [3] where sliding mode controller was designed for spacecraft tracking problems. This was illustrated by an example of multiaxis attitude tracking manoeuvres. An adaptation of the sliding mode control technique was derived and applied to a quaternion-based spacecraft attitude tracking manoeuvres. This modified version presented in [4] is the smoothing model-reference sliding mode control (SMRSMC). This technique improves the transient response and reduces the chatter phenomenon. In [5] the (additive) quaternion-based tracking of spacecraft manoeuvres used sliding mode control in the sense of optimal control. McDuffie and Shtessel [6] designed a de-coupled sliding mode controller and observer for spacecraft attitude control.From the previous literature we conclude that sliding mode control can be used for quaternion-based spacecraft attitude tracking manoeuvres. Floquet [7] presented the stabilization of the angular velocity of rigid body via first-order and second-order sliding mode controllers but it has not been applied to spacecraft tracking problems. Higher-order sliding mode control has desired properties, such as robustness, similar to sliding mode control. It also may reduce chattering and provides better accuracy than first order sliding. Hence we will study spacecraft attitude tracking manoeuvres using higher-order sliding mode control.

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The robust optimal attitude control problem for a flexible spacecraft is considered. Two optimal sliding mode control laws that ensure the exponential convergence of the attitude control system are developed. Integral sliding mode control (ISMC) is applied to combine the first-order sliding mode with optimal control and is used to control quaternion-based spacecraft attitude manoeuvres with external disturbances and an uncertainty inertia matrix. For the optimal control part the state-dependent Riccati equation (SDRE) and optimal Lyapunov techniques are employed to solve the infinite-time nonlinear optimal control problem. The second method of Lyapunov is used to guarantee the stability of the attitude control system under the action of the proposed control laws. An example of multiaxial attitude manoeuvres is presented and simulation results are included to verify the usefulness of the developed controllers.