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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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How this classification was reachedexpand
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) | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".