Constrained control for systems on matrix Lie groups with uncertainties
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Bibliographic record
Abstract
Abstract In this paper, the constrained control of systems evolving on matrix Lie groups with uncertainties is considered. The proposed methodology is composed of a nominal Model Predictive Control (MPC), and a feedback controller. The previous work on the control of systems on manifolds is applied to design the nominal MPC, which generates the nominal trajectory. In the nominal MPC, the state and input constraints on the Lie group are transformed into the constraints on the Euclidean space. While to deal with uncertainties, the feedback control used to track the nominal trajectory is designed directly on the Lie group. The tracking error in the feedback control is proved to be bounded in invariant sets, which are further used to revise the constraints in nominal MPC. We prove that the input‐to‐state stability of the entire system under the proposed control methodology with respect to the disturbances can be achieved. The proposed methodology is applied to the constrained attitude control of rigid bodies with uncertainties. In the application example, the detailed mathematical proof and the comparative numerical simulation are presented to demonstrate the feasibility of the proposed methodology.
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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 | 0.000 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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