Commande mixte <i>H<sub>2</sub>/H<sub>∞</sub></i>. Une approche par la stratégie de Stackelberg
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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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.009 | 0.001 |
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".