An approach to computing bounds on H/sub /spl infin// performance under hard constraints
Bibliographic record
Abstract
A number of standard control problems can be formulated as optimization problems where the goal is to minimize the H/sub /spl infin//-norm of some transfer function while subject to constraints on, for example, system bandwidth or peak sensitivity or output variance. Such constraints usually limit the achievable H/sub /spl infin// performance, but, since the constraints are typically included in the H/sub /spl infin// optimization problem only indirectly through the selection of weights, it is generally not known to what degree the constraints limit the performance. This paper shows how lower bounds on the achievable H/sub /spl infin// norm can be computed for problems where the objective function and constraints can all be written in terms of the sensitivity function. Both pointwise-in-frequency constraints (such as the requirement that the peak sensitivity be limited) and integral constraints (such as the requirement that the output variance be limited when subject to a stochastic disturbance) are dealt with. All constraints are explicitly included in the problem formulation; the solution approach involves optimal curve shaping and is, at least for the single-input single-output case, computationally straightforward.
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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 | 0.000 | 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".