On Stability of Nonlinear Observers Based on Neural Networks
Bibliographic record
Abstract
In this paper, the stability problem of neural network based observers/identifiers for nonlinear systems is revisited when nonlinear-in-parameter neural networks (NLPNN) are employed. The proposed approach is based on decomposing the neural network into two subsystems. The first subsystem (Subsystem 1) consists of the estimation error and output-layer weight error and the second subsystem (Subsystem 2) consists of the hidden-layer weight error. The key to this decomposition is that the hidden-layer weights appear in Subsystem 1, only as an argument of a sigmoidal function and its derivative which are both known to be bounded. This allows us to regard the Subsystem 1 as a linear-in-parameter neural network (LPNN) whose stability proof is more straightforward. Having shown the stability of the first subsystem, the stability of the second subsystem is also shown subsequently without the requirement of having the limiting assumptions of previous work. The bound on estimation error can be made arbitrarily small by proper selection of design parameters. The estimation scheme is then employed to estimate the state of flexible joint manipulators.
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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 | 0.006 |
| 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 | 0.001 | 0.001 |
| Research integrity | 0.001 | 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".