Design of smooth dynamic feedback for stabilization of nonholonomic systems
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Bibliographic record
Abstract
In this paper, a new technique for stabilization of nonlinear (nonholonomic) systems by smooth dynamic feedback is proposed. This technique is based on the authors' design of the smooth (time-invariant) feedback for asymptotic stabilization of a nonholonomic system on the equilibrium manifold. The authors use this feedback, in conjunction with the averaging solution to the nonholonomic motion planning problem, in order to design an explicitly time-dependent dynamic feedback that ensures convergence of the state vector to the state space origin. The authors discuss the advantages of the proposed technique with respect to other comparable approaches. Furthermore, the authors consider a class of chained canonical systems, and demonstrate an interesting and surprising result: a chained system controlled by the time-invariant dynamic feedback formulated in this paper converges to an arbitrary small ball centered at the origin under certain circumstances. Examples and simulations are provided for illustration.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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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