The utilization of closed‐loop prediction for dynamic real‐time optimization
Bibliographic record
Abstract
Real‐time optimization (RTO) is a layer within the hierarchical process automation architecture in which economically optimal set‐points are computed for the underlying plant control system. RTO calculations are traditionally based on steady‐state models, but an increasingly global and dynamic marketplace has led to the development of dynamic RTO (DRTO) strategies. Typical DRTO approaches optimize process input trajectories based on the open‐loop response dynamics of the process, with controller set‐point trajectories constructed from the resulting output response. This paper describes recent developments that utilize closed‐loop prediction in the DRTO calculations for MPC regulated processes. A rigorous closed‐loop DRTO problem is formulated as a multilevel dynamic optimization problem due to the inclusion of a sequence of MPC quadratic programming subproblems to generate the closed‐loop response dynamics. A simultaneous solution strategy is applied in which the MPC subproblems are replaced by their equivalent Karush‐Kuhn‐Tucker (KKT) optimality conditions, permitting reformulation of the original problem as a single‐level mathematical program with complementarity constraints (MPCC). Closed‐loop approximation techniques are proposed to reduce the dimension of the DRTO problem while maintaining good closed‐loop prediction accuracy. The performance of the proposed approaches is illustrated using case studies. Conclusions are drawn, and further research directions identified.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".