The stability analysis of a discrete-time control algorithm for the Canadian advanced nanospace eXperiment-4&5 formation flying nanosatellites
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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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 | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".