Hierarchical control of piecewise affine hybrid systems
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Bibliographic record
Abstract
This paper extends the hierarchical control structures in [4], [6], [17] to the important class of piecewise affine (PWA) hybrid systems. In particular, we extend the notions of dynamical consistency (DC), hybrid in-block controllable (HIBC) partitions and DC partition machines to PWA hybrid systems. Using these notions, we show that if an HIBC partition of the state space is constructed, then controllability of the PWA hybrid system can be easily checked from the associated DC partition machine. Then, we construct the lattice of HIBC partitions and use it to build a hierarchical control structure of the system in which a control objective at any level of abstraction can be realized by state dependent control sequences at the lower levels.
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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 | 0.001 | 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