Extremum Seeking Regulator for a Class of Nonlinear Systems with Unknown Control Direction
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Bibliographic record
Abstract
Nussbaum function techniques are commonly used to investigate output regulation problems for various systems subject to unknown control direction. However, their implementation often leads to large overshoots when the initial estimates of the control direction are wrong, which yields systems with poor transient performance. This study proposes an extremum-seeking control approach to overcome the need for Nussbaum-type functions. The approach yields control laws that can handle the robust practical output regulation problem for a class of nonlinear systems subject to an unknown time-varying control direction. The stability of the design is proven using a Lie bracket averaging technique. It is shown that uniform ultimate boundedness of the closed-loop signals is guaranteed. Finally, a simulation study is performed involving a chaotic control problem for the generalized Lorenz system with an unknown time-varying coefficient to illustrate the validity of the theoretical results.
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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 | 0.000 | 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