Viable cascade control and application to a batch polymerization process
Bibliographic record
Abstract
A hybrid model based on nonlinear control systems and on control affine systems is investigated. For both cases the defining dynamics (or vector fields) at a given time may undergo abrupt changes. Using the framework of viability theory, a controller is proposed that keeps the states within some user-specified region. This desired region is defined by constant bounds on individual states as well as by bounds on state-dependent functions. A viable cascade controller (VCC) is introduced which combines a typical (existing) controller (C) with a viable controller (VC). We assume that a design for C is given. The design of VC is based on computation of the velocity controlled regulation map which provides a set of control inputs that will both keep the states within the viable region as well as prevent these states from approaching the boundary of the viable region at high velocity. Theoretical background for the design of VCC is presented with a simple example which is used to demonstrate some of the computations. This approach is then applied to a batch polymerization process and simulation results are provided.
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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 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| 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".