Stability Analysis of Nonlinear Systems via Estimating Radial-Basis-Function-Network-Based Lyapunov Exponents From a Scalar Time Series
Bibliographic record
Abstract
The concept of Lyapunov exponents is a powerful tool for analyzing the stability of nonlinear dynamic systems especially when the mathematical models of the systems are available. However, for real world systems, such models are often unknown, and estimating these exponents reliably from experimental data is notoriously difficult. A novel method of estimating Lyapunov exponents from a time series is presented in this paper. The method combines the ideas of reconstructing the attractor of the system under study and approximating the embedded attractor through tuning a Radial-Basis-Function (RBF) network, which facilitates the derivation of the Jacobian matrices for applying the model-based algorithm. Simplified as a two-link inverted pendulum with one additional rigid foot-link, a standing biped with a Linear Quadrtic Regulator (LQR) is selected as a case study. The biped balance system has a spectrum including four negative Lyapunov exponents, of which the high numerical accuracy derived through the newly proposed method can be guaranteed even in presence of the measurement noise. We believe that the work can contribute to the stability analysis of nonlinear systems of which the dynamics are either unknown or difficult to model due to complexities.© 2012 ASME
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".