Optimal feedback control of the deployment of a tethered subsatellite subject to perturbations

This paper presents the nonlinear optimal feedback control for the deployment process of a tethered subsatellite model, which involves not only the usually addressed in-plane motion, but also the out-of-plane motion. The model also takes the uncertainties in the mass parameter, the perturbations in initial states, and the external disturbance forces into consideration from an engineering point of view. The proposed controller is on the basis of a shrinking horizon and online grid adaptation scheme. Even though the proposed feedback law is not analytically explicit, it is easy to determine it by using a rapid recomputation of the open-loop optimal control, which generates the initial guesses for controls by interpolating the results from the previous computation. The case studies in the paper well demonstrate the effectiveness, robustness, and dominant real-time merits of the proposed controller.