Discrete‐time mixed ℋ<sub>2</sub>/ℋ<sub>∞</sub>nonlinear filtering
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Bibliographic record
Abstract
Abstract In this paper, we consider the discrete‐time mixed ℋ︁ 2 /ℋ︁ ∞ filtering problem for affine nonlinear systems. Necessary and sufficient conditions for the solvability of this problem with a finite‐dimensional filter are given in terms of a pair of coupled discrete‐time Hamilton–Jacobi‐Isaac's equations (DHJIE) with some side‐conditions. For linear systems, it is shown that these conditions reduce to a pair of coupled discrete‐time algebraic‐Riccati‐equations (DAREs) or a system of linear matrix inequalities (LMIs) similar to the ones for the control case. Both the finite‐horizon and infinite‐horizon problems are discussed. Moreover, sufficient conditions for approximate solvability of the problem are also derived. These solutions are especially useful for computational purposes, considering the difficulty of solving the coupled DHJIEs. An example is also presented to demonstrate the approach. Copyright © 2010 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 | 0.001 | 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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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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