Classical Discrete-Time Adaptive Control Revisited: Exponential\n Stabilization
Bibliographic record
Abstract
Classical discrete-time adaptive controllers provide asymptotic\nstabilization. While the original adaptive controllers did not handle noise or\nunmodelled dynamics well, redesigned versions were proven to have some\ntolerance; however, exponential stabilization and a bounded gain on the noise\nwas rarely proven. Here we consider a classical pole placement adaptive\ncontroller using the original projection algorithm rather than the commonly\nmodifed version; we impose the assumption that the plant parameters lie in a\nconvex, compact set and that the parameter estimates are projected onto that\nset at every step. We demonstrate that the closed-loop system exhibits very\ndesireable closed-loop behaviour: there are linear-like convolution bounds on\nthe closed loop behaviour, which implies exponential stability and a bounded\nnoise gain, as well an easily proven tolerance to unmodelled dynamics and plant\nparameter variation. We emphasize that there is no persistent excitation\nrequirement of any sort.\n
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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 | 0.001 |
| 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 | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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 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".