Some results on l/sub 1/-optimality of feedback control systems: the SISO discrete-time case
Bibliographic record
Abstract
A study is made of the problem of determining when a stabilizing controller is l/sub 1/-optimal for a given plant for some stable weighting function. This problem belongs to the class of inverse problems in optimal control introduced by R.E. Kalman (1964). Only SISO discrete-time plants are considered. The authors give a characterization of all the possible l/sub 1/-optimal compensators for a given plant with different weights under some assumptions on the plant and the allowable weights. A few results are also obtained in the general case (i.e. without making overly restrictive assumptions on the plant and allowable weights). In particular, it is shown that, for a given plant, the set of all the H/sub infinity /-optimal controllers, obtained by considering all stable weighting functions with no zeros on the unit circle, is actually contained in the corresponding set of l/sub 1/-optimal controllers. The authors also show that an l/sub 1/-optimal controller (unlike an H/sub infinity /-optimal controller) can remain l/sub 1/-optimal for the same plant for a wide range of nontrivially different weighting functions. They characterize some of these weighting functions.>
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".