Adaptive LMI-based observer for disturbed nonlinear systems with unknown Lipschitz constant
Bibliographic record
Abstract
This paper presents an adaptive Linear Matrix Inequality (LMI)-based observer designed for Lipschitz continuous nonlinear systems with unknown Lipschitz constants. Moreover, the observer is able to handle state dependent disturbances affecting the system dynamics. In contrast to traditional LMI-based methods that rely on prior knowledge of the Lipschitz constant or bounds on nonlinear functions for observer design, this paper assumes no such information. Instead, the proposed observer adaptively adjusts its gain to accommodate the disturbances and the unknown Lipschitz constant, which can be difficult or even impossible to determine for complex and highly nonlinear functions. The adaptability makes the observer particularly useful for applications where precise knowledge of nonlinear system characteristics is lacking. The observer's asymptotic stability is verified using the Lyapunov stability approach. Finally, the proposed observer is applied to a robotic application, where it is shown to provide accurate state estimation through simulations.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.002 |
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; both teacher heads agree on what is shown here.
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".