Model predictive control formulation for a class of time-varying linear parabolic PDEs
Bibliographic record
Abstract
This paper considers the model predictive control (MPC) formulation for a class of discrete time-varying linear state-space model representations of parabolic partial differential equations (PDEs) with time-dependent parameters. The time-dependence of the parameters are due to the changes in physical properties or operating conditions of the system such as phase transformation, reactor catalyst fouling, and/or domain deformations which arise in many industrial processes. The MPC formulation is constructed for the low dimensional discrete finite-dimensional state space representation of the PDE system and constraints on input and infinite-dimensional state evolution are incorporated in the convex optimization algorithm. The underlying MPC synthesis is utilizing the appropriately defined model representation of the PDE and yields convex quadratic optimization problem which includes input and PDE state constraints. Using the illustrative example of a crystal growth process in which the time-varying property is associated with the evolution of grown crystal, the proposed time-varying MPC formulation is implemented for the optimal crystal temperature regulation problem under the presence of input and state 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 | 0.001 | 0.001 |
| 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".