A Globally Convergent Algorithm for the Run-to-Run Control of Systems with Sector Nonlinearities
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Bibliographic record
Abstract
Run-to-run control is a technique that exploits the repetitive nature of processes to iteratively adjust the inputs and drive the run-end outputs to their reference values. It can be used to control both static and finite-time dynamic systems. Although the run-end outputs of dynamic systems result from the integration of process dynamics during the run, the relationship between the input parameters p (fixed at the beginning of the run) and the run-end outputs z (available at the end of the run) can be seen as the static map z ( p ). Run-to-run control consists in computing the input parameters p * that lead to the reference values z ref . Although a wide range of techniques have been reported, most of them do not guarantee global convergence, that is, convergence toward p * for all possible initial conditions. This paper presents a new algorithm that guarantees global convergence for the run-to-run control of both static and finite-time dynamic systems. Attention is restricted to sector nonlinearities, for which it is shown that a fixed-gain update can lead to global convergence. Furthermore, since convergence can be very slow, it is proposed to take advantage of the mathematical similarity between run-to-run control and the solution of nonlinear equations, and combine the fixed-gain algorithm with a faster variable-gain quasi-Newton algorithm. Global convergence of this hybrid scheme is proven. The potential of this algorithm in the context of run-to-run optimization of dynamic systems is illustrated via the simulation of an industrial batch polymerization reactor.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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