Koopman-based modeling and control of motion systems with hysteresis dynamics using partial state feedback
Why this work is in the frame
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Bibliographic record
Abstract
Koopman operator theory represents nonlinear dynamical systems as linear systems in an extended state-space. By selecting observable functions composed of derivatives and functions of derivatives derived from the system output, it is possible to model the system without requiring knowledge of its internal states. The Koopman observable functions are iteratively refined to achieve close alignment with the original system dynamics . The resulting linear model in the extended space is then incorporated into a linear quadratic tracker (LQT) framework, enabling the system output to track a desired reference signal. The proposed method is demonstrated on a mechanical motion system with Bouc–Wen hysteresis, where the Koopman-based model and LQT provide robust control of the nonlinear system and can track a smooth trapezoidal step-scan trajectory for wafer scanner machines. The controller was also compared to a traditional PID controller , showing improved performance over the trajectory. Furthermore, simulation results demonstrate the controller’s robustness against varying initial conditions, parameter uncertainties, and external disturbances .
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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