Interconnection conditions for the stability of nonlinear sampled-data extremum seeking schemes
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Bibliographic record
Abstract
The application of numerical optimization methods to the problem of extremum seeking control (ESC) has the potential to greatly diversify the types and capabilities of ESC schemes. The first uniform treatment of such sampled-data ESC schemes was given in [1]. We approach the problem from the point of view of interconnected systems' theory, deriving a different, more structurally concrete set of conditions that guarantee the closed-loop stability of such schemes. Our main assumptions concern the interconnection terms arising from the dynamic coupling between a numerical optimization algorithm and a continuous-time nonlinear plant. We demonstrate how these assumptions are satisfied for a special case involving an approximate gradient descent. Our primary motivation in deriving these new conditions is their natural suitability for the development and analysis of decentralized ESC schemes.
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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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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