Stability and Robustness Analysis of Uncertain Nonlinear Systems Using Entropy Properties of Left and Right Singular Vectors
Bibliographic record
Abstract
This paper presents a novel approach to determine the stability space of nonlinear, uncertain dynamic systems that obviates the traditional eigenvalue approach and the accompanying linearizing approximations. In the new method, any long-term dynamic uncertainty is used in an extremely simple and economical way. First, the variability of the design variables about a particular design point is captured through the design of experiments (DOE). Then, corresponding computer simulations of the mechanistic model, over only a small time span, provide a matrix of discrete time responses. Finally, singular value decomposition (SVD) separates out parameter and time information and the expected uncertainty of the first few left and right singular vectors predicts any instability that might occur over the entire life-time of the dynamics. The singular vectors are viewed as random variables and their entropy leads to a simple metric that accurately predicts stability. The stable/unstable spaces are found by investigating the overall design space using an array of grid points of suitable spacing. The length of the time span needed to capture the nature of the dynamics can be as short as two or three periods. The robustness of the stability space is related to the tolerances assigned to the design variables. Errors due to sampling size, time increments, and number of significant singular vectors are controllable. The method can be implemented with readily available software. A study of two practical engineering systems with different distributions and tolerances, various initial conditions, and different time spans shows the efficacy of the proposed approach.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 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) | 0.001 | 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".