Construction of Robust NCR for Input-Constrained Discrete Nonlinear Systems Using Backward Reachability
Bibliographic record
Abstract
In this paper, we address the problem of constructing an under-approximation of the null-controllable region for input constrained discrete nonlinear systems with additive disturbances. The robust null-controllable region (RNCR) refers to the set of states for which robust stabilization is achievable subject to input constraints. In this paper, we propose a computationally tractable algorithm for computation of the robust null-controllable region which involves computation of backward reachable sets, i.e the set of states that can be driven to an given set of states in finite time, subject to disturbances and input constraints. The key ingredient in our RNCR region construction is the efficient computation of backward reachable sets without steps like sequential linearization, guessing of linearization error, etc which are essential part of state of the art backward reachability algorithms. Finally, we demonstrate the efficacy of our algorithm through numerical examples.
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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 | 0.001 | 0.003 |
| 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 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".