Pseudo‐energy shaping for the stabilization of a class of second‐order systems
Bibliographic record
Abstract
SUMMARY A Lyapunov direct method is presented for a class of second‐order systems that includes mechanical systems. This method shall be called a pseudo‐energy shaping method because it reduces to the energy shaping method when a given second‐order system is a mechanical system. The pseudo‐energy shaping method comprehends both the Lyapunov direct method for mechanical systems proposed by Aguilar‐Ibañez and the controlled Lagrangian method that has been successfully applied to stabilize mechanical systems. A class of second‐order systems including mechanical systems is defined first. For this class, matching conditions are derived for the construction of an energy‐like Lyapunov function that shall be called a pseudo‐energy function. Easily verifiable conditions are then presented for stabilizability by the pseudo‐energy shaping method for a class of second‐order linear systems and for a class of second‐order nonlinear systems with one degree of under‐actuation. These results are applied to stabilize a two‐dimensional overhead crane system and a three‐link robot arm system. Copyright © 2011 John Wiley & Sons, Ltd.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".