A Time-varying Feedback Approach to Reach Control on a Simplex
Why this work is in the frame
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Bibliographic record
Abstract
This thesis studies the Reach Control Problem (RCP) for affine systems defined on simplices. The thesis focuses on cases when it is known that the problem is not solvable by continuous state feedback. Previous work has proposed (discontinuous) piecewise affine feedback to resolve the gap between solvability by open-loop controls and solvability by feedbacks. The first results on solvability by time-varying feedback are presented. Time-varying feedback has the advantage to be more robust to measurement errors circumventing problems of discontinuous controllers. The results are theoretically appealing in light of the strong analogies with the theory of stabilization for linear control systems. The method is shown to solve RCP for all cases in the literature where continuous state feedback fails, provided it is solvable by open loop control. Textbook examples are provided. The motivation for studying RCP and its relevance to complex control specifications is illustrated using a material transfer system.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.001 |
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 it