Interior-Point-Based $H_{2}$ Controller Synthesis for Compartmental Systems
Bibliographic record
Abstract
This paper focuses on the optimal <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> controller design for compartmental systems, with the aim of enhancing system robustness while maintaining the law of mass conservation. Through a novel problem transformation, we establish that the original problem is equivalent to a new non-convex optimization problem with a closed polyhedral constraint. Existing works have developed various first-order methods to tackle inequality constraints. However, they often lack convergence guarantees in non-convex scenarios, thereby reducing their reliability in practical applications. Consequently, there is a critical need to develop new and efficient algorithms with convergence guarantees. In this paper, we reformulate the problem using log barrier functions and introduce two separate approaches with convergence guarantees to address the problem: the first-order interior point method (FIPM) and the second-order interior point method (SIPM). Additionally, we propose an initialization method to guarantee the interior property of initial values. Finally, we compare FIPM and SIPM through a room temperature control example and illustrate their pros and cons via simulations. They are also compared to the existing alternating direction method of multipliers (ADMM) across different system scales.
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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) | 0.001 | 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".