Optimal feedback control of stochastic systems on Hilbert spaces based on compact sets in the space of Hilbert-Schmidt operators
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Bibliographic record
Abstract
In this paper we present necessary and sufficient conditions characterizing compact sets in the spaces of Nuclear and Hilbert-Schmidt operators on Hilbert spaces.Based on these results, we also characterize compact sets in the space of probability measures on separable Hilbert spaces.These results are then used in the study of optimal feedback control theory for stochastic systems.We prove existence of optimal feedback control laws for standard and several nonstandard control problems.Further, we present necessary conditions of optimality and an algorithm and related convergence theorem whereby optimal control laws can be constructed.We present also a result characterizing compact sets in the space of probability measures on separable Hilbert spaces.These results have interesting applications in control theory on infinite dimensional Banach spaces as presented in the last section.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| 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 | 0.000 |
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.
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