The general station-keeping problem is a focal topic when considering any spacecraft mission application. Recent missions are increasingly requiring complex trajectories to satisfy mission requirements, necessitating the need for accurate station-keeping controllers. An ideal controller reliably corrects for spacecraft state error, minimizes the required propellant, and is computationally efficient. To that end, this investigation assesses the effectiveness of several controller formulations in the circular restricted three-body model. Particularly, a spacecraft is positioned in a L₁ southern halo orbit within the Sun-Earth Moon Barycenter system. To prevent the spacecraft from departing the vicinity of this reference halo orbit, the Floquet mode station-keeping approach is introduced and evaluated. While this control strategy generally succeeds in the station-keeping objective, a breakdown in performance is observed proportional to increases in state error. Therefore, a new hybrid controller is developed which leverages Floquet mode and reinforcement learning. The hybrid controller is observed to efficiently determine corrective maneuvers that consistently recover the reference orbit for all evaluated scenarios. A comparative analysis of the performance metrics of both control strategies is conducted, highlighting differences in the rates of success and the expected propellant costs. The performance comparison demonstrates a relative improvement in the ability of the hybrid controller to meet the mission objectives, and suggests the applicability of reinforcement learning to the station-keeping problem.

Indiana University-Purdue University Indianapolis (IUPUI) / Open quantum systems have become a rapidly developing sector for research. Such systems present novel physical phenomena, such as topological chirality, enhanced sensitivity, and unidirectional invisibility resulting from both their non-equilibrium dynamics and the presence of exceptional points. We begin by introducing the core features of open systems governed by non-Hermitian Hamiltonians, providing the PT -dimer as an illustrative example. Proceeding, we introduce the Lindblad master equation which provides a working description of decoherence in quantum systems, and investigate its properties through the Decohering Dimer and periodic potentials. We then detail our preferred experimental apparatus governed by the Lindbladian. Finally, we introduce the Liouvillian, its relation to non-Hermitian Hamiltonians and Lindbladians, and through it investigate multiple properties of open quantum systems.

<p>Open quantum systems have become a rapidly developing sector for research. Such systems present novel physical phenomena, such as topological chirality, enhanced sensitivity, and unidirectional invisibility resulting from both their non-equilibrium dynamics and the presence of exceptional points.</p> <p><br></p> <p>We begin by introducing the core features of open systems governed by non-Hermitian Hamiltonians, providing the PT -dimer as an illustrative example. Proceeding, we introduce the Lindblad master equation which provides a working description of decoherence in quantum systems, and investigate its properties through the Decohering Dimer and periodic potentials. We then detail our preferred experimental apparatus governed by the Lindbladian. Finally, we introduce the Liouvillian, its relation to non-Hermitian Hamiltonians and Lindbladians, and through it investigate multiple properties of open quantum systems.</p>