Nonlinear robust H_∞ tracking control for 6 DOF spacecraft formation with input saturation

In this paper, the problem of robust H_∞ tracking control for 6 DOF spacecraft formation flying in the presence of parameter uncertainties, external disturbances and input saturation is addressed. Firstly, a robust H_∞ controller constructed by the solution of the Hamilton-Jacobi-Inequality(HJI) is proposed. It is proved that the coupled 6 DOF tracking error system is stable and robust in respect to parameter uncertainties, and the H_∞ norm between external disturbance and regulated output is ensured to be no more than a prescribed attenuation level. Subsequently, to find the solution of the HJI, the state dependent Riccati inequality (SDRI) method is applied, which is an effective approximation approaches by solving an algebraic Riccati inequality for each state online through the LMI tool instead of solving partial differential inequality directly. The robust H_∞ controller based on the SDRI method not only has a simple structure, but also can be designed flexibly with state dependent coefficient (SDC) parameterizations selected. Further, the SDRI method can be utilized flexibly to deal with the nonlinear constrained on the control input by augmenting the original system. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed controller.