Computing maximal invariant sets for switched nonlinear systems
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Bibliographic record
Abstract
Invariant sets play a fundamental role in the analysis and control design of dynamical systems. In this paper, we consider computation of maximal invariant sets for discrete-time switched nonlinear systems. Switched nonlinear systems are described as a family of nonlinear systems with a discrete variable that decides which mode will be active at a specific time. We consider two scenarios: one leads to the computation of switching controlled invariant sets and the other leads to computation of invariant sets subject to arbitrary switching. The main result of the paper establishes that the outer approximations computed using interval analysis indeed converge to the maximal invariant sets for general switched nonlinear systems without any stability assumptions. The proposed method is illustrated with nonlinear systems with polynomial dynamics.
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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 | 0.000 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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