An Observer-Based Extremum Seeking Controller Design for a Class of Second-Order Nonlinear Systems
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Bibliographic record
Abstract
In this letter, an extremum seeking controller (ESC) is designed for stabilization and output minimization for a class of second-order control-affine nonlinear systems. The main difficulty with such design lays in the fact that the relative degree between the measured output and the system’s input is two. As a result, the classical ESC approaches which use a high-pass filter for differentiation, are not suitable. We propose a perturbation-based controller in the feedback loop that utilizes a high-gain like observer with bounded derivatives of first and second-order. The closed-loop system is shown to be practically stable while maintaining the output in a small neighborhood of its optimum value. Simulation results demonstrate the effectiveness of the proposed approach.
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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 | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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