Euclidean space controllability conditions and minimum energy problem for time delay systems with a high gain control
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Bibliographic record
Abstract
In this paper, a non-autonomous differential system with state delays and with a large coefficient for the control (high gain control) is considered. By a proper control transformation, this system is converted into equivalent time delay system singularly perturbed by a small positive parameter. The latter system, is decomposed asymptotically into two much simpler parameter-free subsystems, slow and fast ones. The slow subsystem has delays in the state and control variables, while the fast subsystem is delay-free. Based on the assumption of the Euclidean space controllability of the slow subsystem, the Euclidean space controllability of the transformed and original systems is established for all sufficiently small values of the parameter of singular perturbation. Also, the minimum energy control problem for the transformed system is considered. Asymptotic behaviour with respect to the small parameter of the solution to this problem is studied. An illustrative example is presented.
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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 | 0.000 | 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