Adaptive boundary observer network design for the consensus on the estimation of a class of parabolic partial differential equation systems
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Bibliographic record
Abstract
Abstract This work develops a network of adaptive boundary observers and studies the agreement between state and parameter estimates for a single target parabolic partial differential equation (PDE) system in the presence of structured and unstructured uncertainties. It is assumed that the unknown parameters take the form of either a structured uncertainty with unknown constant parameters or an unstructured uncertainty that can be neutralized by a radial basis function neural networks with unknown weights. The proposed adaptive observers consisting of agents in the network follow the structure of adaptive identifiers for the considered target PDE systems with the insertion of a penalty term in both the state and parameter estimates. Different from earlier efforts, the proposed adaptive laws include a penalty term of the mismatch between the parameter and state estimates generated by the other adjacent agents, which helps to accelerate the estimation of uncertainties. Additionally, the effects of these modifications on the agreement amongst the state and parameter estimates are investigated. Theoretical proofs are provided to show that the proposed approach guarantees the exponential convergence of estimation errors in the case of structured uncertainties and the ultimate boundedness of estimation errors in the case of unstructured uncertainties. Finally, numerical simulations are carried out to verify the effectiveness of the design methods.
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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 | 0.000 |
| 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 | 0.000 |
| 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