Geometric based estimation and nonlinear PI controller for dynamic optimization problem
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Bibliographic record
Abstract
In this paper, the minimization of an unknown but measurable cost function of the state variables of nonlinear systems governed by uncertain dynamics is considered. An extremum-seeking algorithm is proposed to solve this uncertain dynamic optimization problem without the need for a time-scale separation. The Lie derivatives of the convex cost function with respect to nonlinear dynamics of the system are regarded as time-varying parameters. A new technique based on the concept of invariant manifolds is proposed for the adaptive estimation of the time-varying parameters. A nonlinear proportional-integral approach is then used to formulate the extremum-seeking controller. This approach is shown to avoid the need for a time-scale separation in real-time optimization problem. The effectiveness of the proposed method is illustrated with a simulation example.
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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