Bibliographic record
Abstract
Summary This paper presents a solution of the optimal control problem for a class of pseudo Euler‐Lagrange systems and proposes a systematic approach to find a Lyapunov function for stability analysis and controller synthesis for such systems. There are three main contributions of the paper. First, a systematic procedure is proposed and proved to construct a Lyapunov function for pseudo Euler‐Lagrange system directly from the mathematical structure of the differential equations, without the need to determine any kinetic or potential energy of the system first. Second, control methodologies for pseudo Euler‐Lagrange systems are also developed. In particular, an optimal controller is found for the case of second order dynamics yielding the same structure for the closed‐loop Lyapunov function as the one derived from the systematic procedure outlined as the first contribution. Finally, the optimal control methodology is extended to systems with order higher than two for a class of triangular systems. The method proposed here works for any mathematical model in the class of pseudo Euler‐Lagrange systems and is therefore not restricted to models of physical systems. Several examples illustrate the application of the novel approach, including mass‐spring‐damper systems and Van der Pol oscillators. Copyright © 2016 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) | 0.000 | 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 | 0.001 |
| 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".