State feedback output regulation for a class of hyperbolic PDE systems
Bibliographic record
Abstract
This work focuses on the development of a state feedback regulator for a class of first order hyperbolic PDE systems with spatially varying coefficients and single point observation. The plant is assumed to be exponentially stabilizable and driven by a linear finite dimensional exosystem which is neutral stable and generates the reference signal and disturbance for the plant. The regulator design problem is to control the fixed plant such that the plant output tracks the reference signal and/or rejects the disturbance. Under the standard assumption of stabilizability, this work shows that the solvability of a constrained Sylvester equation is sufficient to guarantee the solvability of the regulator problem. Moreover, the Riccati and Lyapunov equations are utilized to provide a choice of stabilizing feedback gain which guarantees the closed-loop stability. An adequate numerical example of constant tracking for the first order hyperbolic PDE system with spatially varying coefficients is explored within the proposed regulator 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 | 0.000 | 0.001 |
| 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 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".