On‐Line Feedback Control for Optimal Periodic Control Problems
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Bibliographic record
Abstract
Abstract In this paper a method for generating periodic orbits for a class of non‐linear systems is presented. A periodic Hamiltonian system is defined as the target equilibrium for non‐linear systems in strict feedback form. A parameter dependent non‐linear periodic system description is introduced for a two‐dimensional subsystem and extended to higher dimensions using backstepping. Extremum seeking is used as a parameter update law that guarantees the convergence of the system to the optimal periodic orbit with respect to a given parameterization. The procedure resulted in an on‐line feedback control implementation that typically steers the system to a suboptimal solution that nevertheless improves the static optimization solution. Typical examples from optimal periodic control literature are used to illustrate the application of this 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 | 0.001 | 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 | 0.001 |
| 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