Constrained Extremum Seeking Controller Design for a Class of Second-Order Nonlinear Systems
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Bibliographic record
Abstract
This paper investigates the problem of stabilization and output minimization for a class of second-order nonlinear systems with state constraints. We show that integrating a model-based extremum seeking controller (ESC) within the feedback loop guarantees that both the system output and trajectories asymptotically reach their optimal values. Furthermore, we prove the forward invariance of the safe set by employing the notion of high-order barrier functions (HOBF), enforced through saddle point dynamics. Using modified high-gain observers and high-frequency perturbations, we present a control algorithm that estimates the unknown dynamics of the nonlinear system solely based on measurements of the cost function and constraints. Simulation results demonstrate the algorithm’s effectiveness in steering the system response towards its optimum while avoiding unsafe region.
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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) | 0.000 | 0.000 |
| 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 | 0.000 | 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