The stability analysis of a discrete-time control algorithm for the Canadian advanced nanospace eXperiment-4&5 formation flying nanosatellites
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Bibliographic record
Abstract
The development of an LQR-based control algorithm for the Canadian advanced nanospace eXperiment (CanX)-4&5 formation flying nanosatellite mission is described. To facilitate an analytical stability proof of the algorithm, elements of the non-linear and continuous system are linearized and discretized. A suitable state for the system is selected and the algorithm is converted into a discrete linear time-varying system that is very nearly periodic. The stability of the system is then determined by means of discrete Floquet theory. This analysis is applied to the CanX-4&5 algorithm during its primary mission of testing along track orbit formations and projected circular orbit formations. The analysis is also applied to the algorithm while executing a quasi J 2 -invariant formation. The results in all cases indicate stability. Finally, for the quasi J 2 -invariant formation the control authority of the algorithm is reduced until the stability limit is approached and the minimum Δ V required to maintain the formation is found.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it