Control strategies for stable orbits around phobos
Bibliographic record
Abstract
This study compares three linear optimal controllers for stationkeeping with respect to reference orbits around Phobos. The dynamics of the Mars-Phobos system are constrained to the synodical plane of the circular restricted three-body problem (CRTBP) with Phobos modelled as an ellipsoid. The controllers rely on periodic orbits which permit the dynamics to be expressed as a linear system with periodic coefficients. A novel method of determining the necessary conditions for periodic orbits is formulated through nonlinear optimization techniques, where the function to be minimized is the vector norm of the difference between the initial and final conditions of the orbit. The optimization algorithm is a Nelder-Mead simplex and is shown to outperform any gradient-based methods as well as other techniques for determining such orbits. Two controllers, constant feedback and scheduled, are developed from the algebraic Riccati equation (ARE), which is solved at specific points on the reference orbits. These controllers are then compared to the optimal solution which uses the time-varying Riccati equation. At high orbits, the periodicity of the linearized system is very small and the controllers are nearly identical in performance. Closer orbits reveal increases in the periodicity of the dynamics, leading to an increase in performance of the time-varying Riccati equation-based controller over the scheduled and constant feedback gain cases
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".