Optimization of Linear Multivariable Systems with Structured Perturbations and Prescribed Closed-Loop Eigenvalues
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Bibliographic record
Abstract
In this article the conventional linear quadratic regulator (LQR) problem is modified to include a third term penalizing state trajectory deviations. The modification is motivated by the tendency of system parameters to assume different values rather than their nominal ones due to components aging, number truncation, and other factors. The proposed optimal controller not only results in an explicit solution to the modified LQR problem, but also allows the designer to assign the closed-loop eigenvalues to prespecified locations. The proposed controller permits the designer to consider undesired variations in both system matrices (A, B) and also to assign the closed-loop eigenvalues to some desired locations. This eigenvalues assignment is achieved without imposing any restriction either on their nature, multiplicity, or their open- or closed-loop locations in the complex plane.
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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) | 0.001 | 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