Stabilization of a Class of Second-Order Nonlinear Systems Using Extremum Seeking Control
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Bibliographic record
Abstract
In this paper, we address the problem of stabilization and output minimization for a class of second-order nonlinear systems in input-affine form. We first introduce a target (ideal) controller that stabilizes the equilibrium of the closed-loop system while minimizing a measured cost function taken as the system’s output. Building on this, we propose an extremum-seeking controller that relies solely on output measurement. We demonstrate that, with an appropriate choice of controller parameters, the nominal system under output feedback exhibits behaviour similar to the target system. This is used to prove that the extremum seeking controller achieves the stabilization of the unknown system to the unknown steady-state optimum of the measured cost function. The effectiveness of the proposed algorithm in optimization and output regulation is illustrated through two numerical examples.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| 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