Boundary model predictive control of thin film thickness modelled by Kuramoto-Sivashinsky equation with input and state constraints
Bibliographic record
Abstract
In this work, a model predictive control (MPC) synthesis is proposed to regulate, in the presence of naturally present state and input constraints, the thickness of falling film in the vertical tube, modelled by the Kuramoto-Sivashinsky (K-S) equation. The infinite-dimensional state space representation is developed and an exact transformation modifies the boundary control problem into the distributed control problem. The appropriate analysis of K-S spectral operator reveals dissipative structure of the linearized operator which benefits from the applicability of spectral decomposition for the control purpose. The model predictive control synthesis utilizes the finite dimensional representation of the K-S PDE state in the formulation of the optimization functional, while the infinite dimensional K-S PDE state constraints are appropriately defined and cast in a form of constrained quadratic optimization. The simulation study evaluates the performance of proposed methods which achieves both stabilization of the thin film thickness and obeys inputs and states constraints.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".