Output-Only Identification of Lur’e Systems with Prandtl-Ishlinskii Hysteresis Nonlinearities
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Bibliographic record
Abstract
Lur’e systems are dynamical systems that are characterized by the feedback interconnection between a linear, time-invariant system and a feedback nonlinearity. Lur’e systems have been used to characterize the dynamics of several systems including gas turbine combustors and self-oscillatory systems. In this paper, we introduce an Identification algorithm for Lur’e systems with hysteretic feedback nonlinearities. We assume that the input to the Lur’e system is an unknown constant signal, and the linear dynamics have nonzero initial conditions. First, we use least squares with a transfer function model to identify the linear dynamics of the Lur’e system. Then, we use the identified linear dynamics along with the measured output to construct an estimate of the hysteretic nonlinearity. We show numerical examples to illustrate 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 | 0.000 | 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