Dual approaches to strictly positive real controller synthesis with a performance using linear matrix inequalities
Bibliographic record
Abstract
SUMMARY The synthesis of controllers that minimize a performance index subject to a strictly positive real (SPR) constraint is considered. Two controller synthesis methods are presented that are then combined into an iterative algorithm. Each method synthesizes optimal SPR controllers by posing a convex optimization problem where constraints are enforced via linear matrix inequalities. Additionally, each method fixes the controller state‐feedback gain matrix and finds an observer gain matrix such that an upper bound on the closed‐loop ‐norm is minimized and the controller is SPR. The first method retools the standard ‐optimal control problem by using a common Lyapunov matrix variable to satisfy both the criteria and the SPR constraint. The second method overcomes bilinear matrix inequality issues associated with the performance and the SPR constraint by employing a completing the square method and an overbounding technique. Both synthesis methods are used within an iterative scheme to find optimal SPR controllers in a sequential manner. Comparison of our synthesis methods to existing methods in the literature is presented. Copyright © 2012 John Wiley & Sons, Ltd.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".