Handling Inequality Constraints in Optimal Control by Problem Reformulation
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Establishment of optimal control for systems, where constraints involve both control and state, is very difficult. In some problems the difficulty is reduced significantly by transforming the optimal control problem. For illustration, the optimal control of a nonisothermal fed-batch reactor with heat removal constraint is considered. Although there are only two control variables, the feed rate and the temperature, the heat removal rate constraint makes the optimal control problem very difficult. To parametrize the optimal control problem, the time interval is divided into P time stages of variable length, and piecewise constant control is used at each time stage. Establishment of the optimal control policy is very challenging owing to the low sensitivity, the heat removal constraint, and the need for a large number of time stages for adequate approximation. However, by reformulating the optimal control problem where heat generation, rather than temperature, is used as a control variable, we are able to get greater accuracy with a smaller number of time stages. The optimal control policy is established with iterative dynamic programming and checked with LJ-optimization procedure.
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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 | 0.001 |
| 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