Data-driven optimal controller design for sub-satellite deployment of tethered satellite system

In the paper, we presented a data-driven optimal control method for the sub-satellite deployment of tethered satellite systems during the release phase, with the objective of reducing the libration angle fluctuation during system work. First, the dynamic equation of the tethered satellite system was established and processed dimensionless. Considering the presence of noise when sensors were put on the satellite to measure the libration angle, the corresponding state equation was derived. Next, we estimated the system state using an unscented Kalman filter and established a performance index and the Hamilton function. Based on the index, we designed an optimal control strategy and provided sufficient conditions for the asymptotic stability of the closed-loop system. We used critic actor neural networks based on measurement data to implement the data-driven control algorithm to approximate the performance index function and the control policy, respectively. Finally, taking a tethered satellite system as an example, a simulation showed that the unscented Kalman filter can effectively estimate the system state and improve the impact of noise on the system, and the proposed optimal control strategy ensured that the tethered satellite system is stable, which shows the applicability and effectiveness of the control strategy in reducing the tether vibration of the disturbed system.