2‐DOF discrete‐time nonlinear ℋ<sub>∞</sub>‐filters
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Bibliographic record
Abstract
Abstract In this paper, a new theory of two‐degrees‐of‐freedom (2‐DOF)‐ℋ︁ ∞ and certainty‐equivalent filters is presented. Exact and approximate solutions to the nonlinear ℋ︁ ∞ filtering problem using this class of filters are derived in terms of discrete‐time Hamilton–Jacobi–Isaacs equations. The expressions for the filter gains are determined as functions of the filter state and the system's output in contrast to earlier results. Hence, it is shown that coupled with the additional degree‐of‐freedom, these filters are a substantial improvement over the earlier 1‐DOF case. The theory presented is also generalized to n ‐DOF filters, which bore strong connections to linear infinite‐impulse response filters and hence are generalizations of this class of filters to the nonlinear setting. Simulation results are also given to show the usefulness of the new approach. Copyright © 2009 John Wiley & Sons, Ltd.
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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) | 0.000 | 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