Multi-Estimator Based Adaptive Control which Provides Exponential Stability: The First-Order Case
Bibliographic record
Abstract
Classical adaptive controllers provide asymptotic stabilization; neither exponential stability nor a bounded noise gain is typically proven. In recent work it is shown that these desired properties can be achieved by using an estimator based on the original ideal Projection Algorithm (together with a restriction of the parameter estimates to a given compact convex set), rather than the commonly used modified classical algorithm. Here the goal is to remove the convexity requirement. To this end, we consider the first-order case with unknown plant parameters belonging to a compact uncertainty set of controllable pairs. The first step of our approach is to observe that the compact uncertainty set can be covered by a finite number of convex compact sets, each of controllable pairs. For each of the convex compact sets, we design an estimator together with the corresponding one-step-ahead controller, and apply a switching logic to choose between them. We prove that the resulting controller guarantees linear-like convolution bounds on the closed-loop behavior, which implies exponential stability and a bounded noise gain.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| 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) | 0.001 | 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".