Exponential super-twisting control for nonlinear systems with unknown polynomial perturbations
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Bibliographic record
Abstract
The study focuses on the control of nonlinear dynamic systems in the presence of parameter uncertainties, unmodeled dynamics, and external disturbances. The lumped perturbation is assumed to be bounded within a polynomial in the system state with the polynomial parameters and degrees unknown a priori such that it accommodates a quite wider range dynamic systems. Based on the studies in recent super-twisting algorithm designs and the idea from adaptive sliding mode control for nonlinear systems with uncertainties, we propose a novel adaptive super-twisting algorithm with exponential reaching law, or exponential super-twisting algorithm (ESTA), for the high-stability and acceptable accuracy control of the aimed nonlinear dynamics. The stability analysis and practical finite-time (PFT) convergence are proven using Lyapunov theory and an intuitive analysis of the control behaviour. Simulations are performed to compare the proposed ESTA with the existing super-twisting method and the traditional proportional integral differential control. The simulation results demonstrate the effectiveness of the proposed ESTA in terms of the fastest settling time and the smallest overshoot.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 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