Input-to-state stabilisation of 1-D time-varying parabolic PDEs involving Dirichlet boundary disturbances by static backstepping control
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
This paper addresses the problem of input-to-state stabilisation for a class of time-varying parabolic PDEs with Dirichlet and Robin boundary disturbances, as well as in-domain disturbances. A static backstepping boundary feedback control employing a time-invariant kernel function is developed, which allows significantly reducing the computational burden in controller design and implementation. The so-called generalised Lyapunov method is applied in the assessment of the input-to-state stability (ISS) of parabolic PDEs, which, compared to the non-Lyapunov methods, considerably eases the establishment of the ISS with respect to the Dirichlet and Robin boundary disturbances in the spatial Lp-norm for the closed-loop system whenever p∈[2,∞). Numerical simulations are conducted to illustrate the validity of the controller and the obtained theoretical results.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.001 |
| 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 it