Maria Khodaverdian

To address the challenges of controlling flexible spacecraft with nonlinear dynamics, we propose a Koopman-based approach that represents these dynamics in a space of an infinite-dimensional observable that facilitates analysis and control design. Unlike conventional data-driven techniques, which often struggle to identify suitable observables, our method systematically derives tailored observables specifically designed for flexible spacecraft dynamics. We prove that the proposed sequence of observables tends to zero pointwise, enabling a finite subset to accurately approximate the lifted space. Numerical simulations validate the agreement between the lifted dynamics and the original nonlinear spacecraft model. By leveraging this Koopman-based approximation, we enable the design of Model Predictive Control (MPC) and linear quadratic regulator controllers for nonlinear dynamics, effectively simplifying discrete control synthesis. We benchmark our method against both nonlinear MPC and linear MPC applied directly to the nonlinear system, demonstrating the effectiveness of our proposed framework.

In this article, two dual-loop control methods are proposed for attitude control and reaction wheels momentum management of the spacecraft simulator by assimilating the advantages of sliding mode and model predictive control (MPC). In the first method, by utilizing the high accuracy and constrained features of the MPC, an optimal controller is designed in the inner loop. MPC drives the angular velocity to the desired value while keeping the reaction wheel velocity to a small region near the origin, considering the constraints of the actuators. Furthermore, based on the fixed-time terminal sliding mode (TSM) the proper angular velocity is produced in the outer layer of this composite controller for the MPC part. In the second method, contrary to the first one, in the exterior loop MPC and in the interior loop finite-time TSM have been designed. The incorporated twofold nonlinear controllers’ policy insures a good dynamic and robustness against external disturbances. The high yielding of the control algorithms has been analyzed by simulation and experimental validation utilizing MATLAB software with real-time connection based on LabVIEW.