Optimal attitude consensus control for rigid spacecraft formation based on control Lyapunov functions

Abstract

Abstract In this article, the optimal attitude consensus control problem of distributed spacecraft formation through local information exchange is solved in the presence of parameter uncertainty and disturbance. The attitude dynamics model of rigid spacecraft formation is established based on unit quaternion under an undirected graph. Then, the optimal attitude consensus control scheme based on control Lyapunov functions is adopted for rigid spacecraft formation. The approach to construct an appropriate Lyapunov function for multiple spacecraft is developed. Then the lumped disturbance is estimated by an extended state observer (ESO) and using the sliding mode control approach improves the robustness of the controller. The proposed optimal controller can not only ensure the global consensus convergence of the system but also make the preset performance index function achieve the minimum value. In addition, the mathematical proof is given for the stability analysis of the system by the Lyapunov stability theory. Finally, some simulations and comparisons are presented to demonstrate the validity and advantages of the proposed controller.

Keywords

• aerospace control
• attitude control
• distributed control
• Lyapunov methods
• non‐linear control systems
• optimal control