Convex Inner Approximation for Mixed $H_2$/$H_\infty$ Control With Application to a 2-DoF Flexure-Based Nanopositioning System
Bibliographic record
Abstract
This article presents a convex inner approximation approach for mixed${H}_2$/${H}_\infty$control of a flexure-based nanopositioning system. Generally for such positioning systems, the inevitable existence of model mismatch renders it often times difficult-to-achieve satisfying system performance. Additionally, it is essential to also note that the high-order resonances typically presented are prone to be activated if the controller is not designed appropriately, especially in the case when the control input variation arising from the design is unnecessarily drastic. Therefore, to circumvent the above undesirable possibilities, this work aims to improve the tracking performance with a suitable controller design that effectively suppresses the control input variation. Furthermore, despite the existence of model uncertainties, it is shown that it is possible for a subset of stabilizing controller gains to be characterized appropriately via convex inner approximation, which then further facilitates the determination of the controller by means of convex optimization. Rather importantly, this approach provides a performance guarantee with an optimized limiting bound to the$H_2$-norm level (which assures optimal behavior for the system), and also concurrently limits the$H_\infty$-norm level within a prescribed attenuation level (which satisfies a prescribed robustness measure). Finally, numerical optimization and comparative experiments are carried out for demonstrative purposes.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.002 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".