Hybrid State Space and Frequency Domain System Level Synthesis for Sparsity-Promoting H<sub>2</sub>/H<sub>∞</sub> Control Design
Bibliographic record
Abstract
Design of optimal linear feedback controllers is a challenging but important problem in many applications. The main difficulties arise from nonconvexity and infinite dimensionality of the associated optimization problem for the design. A promising recent approach to address these challenges is to first use system level synthesis to render the problem convex using a clever reparameterization, and then to apply an approximation by simple poles to obtain a finite dimensional problem. However, when computing ${\mathcal{H}}_{2}$ and ${\mathcal{H}}_{\infty}$ norms, this prior approach requires an additional approximation of a finite time horizon for the closed-loop impulse response. This finite horizon results in increased suboptimality, degraded performance, and increased problem size and memory requirements. To address these limitations, we present a novel control design framework that combines the frequency domain system level synthesis constraints with a state space formulation of the ${\mathcal{H}}_{2}$ and ${\mathcal{H}}_{\infty}$ norms using linear matrix inequalities. This state space formulation eliminates the need for a finite time horizon approximation, and results in a convex and tractable semidefinite program for the control design. To preserve robustness, in practice it is important that controllers only contain a relatively small number of poles. Therefore, we propose to make an optimal sparse selection of simple poles from a large initial collection to maintain robustness while improving performance. As this sparsity constraint is nonconvex, we use group lasso regularization to enforce sparsity while maintaining convexity for the control design. Finally, the superior performance of the proposed method is illustrated on an example of power converter control design.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| 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) | 0.004 | 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".