Commande mixte <i>H<sub>2</sub>/H<sub>∞</sub></i>. Une approche par la stratégie de Stackelberg
Why this work is in the frame
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Bibliographic record
Abstract
Mixed H 2 /H ∞ control corresponds to design a control minimizing a system H 2 norm with respect to a sub-optimal constraint on a H ∞ norm. This is an open field of research, despite the abundance of approach in the literature. This paper uses a game theoretic approach to formalize the management of different criteria (one for H 2 norm and one for H ∞ norm). Even if this approach was already used with Nash strategy in the literature, we propose here to use Stackelberg strategy, which is adapted to manage different criteria with a hierarchy between them. Necessary conditions for a finite time horizon are developed and lead to a singular (cheap) control. This property is interpreted in game theoretic terms: Stackelberg strategy degenerates in Nash strategy. By using conjugate times theory, we emphasize that these conditions are also sufficient. Some numerical example illustrates our approach.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| 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