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The control problem of underactuated spacecraft chaotic attitude motion is investigated based on exponential reaching law in this paper. First, the underactuated spacecraft chaotic attitude system is written in nonlinear equation form with two controls. Once the trajectory planning of angular acceleration is preset, the dynamics equation of angular velocity error can be obtained. Then, the sliding mode controller based on exponential reaching law and linear matrix inequality is designed, which consists of equivalent control term and switching control term. Finally, simulations are performed to test the performance of the proposed controller.

A novel model of space electromagnetic docking is established to solve the problem of traditional plume contamination and short service life in this paper. A new modelling technique regarding space electromagnetic docking for CubeSat is proposed. The mathematical model with four core-containing energized solenoids is derived and simplified to the magnetic dipole far-field model of single-turn coil. Simplifying the magnetic dipole far-field model will yield the model of space electromagnetic docking, and the numerical simulation results also verify the reliability and feasibility of simplification process.

This paper investigates the design method of full order state observer for satellite attitude control system using mixed H 2 /H ∞ optimal approach. A linear system described by state space form is introduced first to state the problem of full order state observer design. The designed observer should meet the requirement of H 2 performance and H ∞ performance so that the disturbance would influence the observer as little as possible. Thus, we convert the satellite attitude control system to the same state space form, and deduce the mixed H 2 /H ∞ approach based on linear matrix inequalities (LMIs). By solving LMIs, we can obtain the solution of corresponding convex optimization problem. Then, the observer gain can be decided. The simulation results based on satellite attitude control system show that the magnitude of observer error is 10−6 rad/s within 10000s. We can conclude that the mixed H 2 /H ∞ approach of full order state observer design is effective and the external disturbance has little influence on the observation error.

Due to the space missions' limited budget, microsatellite would be an economical choice, so there has been a great decrease in size and weight. Micro satellite is vulnerable to space environmental disturbances and perturbation of controller. As to the multiplicative perturbation in attitude controller, this paper investigates a robust H ∞ controller design with model uncertainties and subject to external disturbances and controller's multiplicative perturbations. By using linear matrix inequality (LMI) method, the numerical solution of state feedback controller in terms of multiplicative perturbation can be efficiently solved. The performance differences between the non-fragile control and the mixed H 2 /H ∞ control without considering controller's multiplicative perturbation are discussed in detail. The attitude control design taking controller perturbation into account shows excellent effectiveness with respect to simulation results.