Performance Analysis of Second-Order Sliding-Mode Control Systems With Fast Actuators
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Bibliographic record
Abstract
The robustness of the second-order sliding-mode control (2-SMC) algorithm known as the "generalized sub-optimal" algorithm is analyzed with respect to the cascade introduction of a linear fast actuator. It is shown that if the actuator dynamics are sufficiently fast then the system trajectories converge to an invariant set that includes the second-order sliding domain s = s' = 0. It is also shown that the size of the invariant set has quadratic dependence with respect to the actuator "small parameter" mu for the sliding variable s, and linear dependence for its derivative s. This means that in the steady state the system trajectories converge to an invariant domain described by the following conditions: |s| les O(mu <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) and |s| les O(mu). A simulation example is given to confirm the proposed.
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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 | 0.001 | 0.001 |
| 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