Robustly Complete Reach-and-Stay Control Synthesis for Switched Systems via Interval Analysis
Bibliographic record
Abstract
This paper proposes a formal synthesis algorithm for discrete-time switched systems with respect to reach-and-stay specifications. Fundamental to the proposed method is a fixed-point algorithm characterizing the initial states satisfying reach-and-stay specifications for continuous-state systems. Based on the interval branch-and-bound scheme, the original continuous state space is adaptively partitioned into a finite number of cells according to the given specification and system dynamics during the fixed-point iterations. Valid switching modes are recorded and a partition-based switching strategy can be extracted immediately after the algorithm terminates. In contrast with most of the abstraction-based methods, the proposed algorithm is guaranteed to return a switching strategy after a finite number of iterations, provided that the specification is robustly realizable. As illustrated in the numerical example, the adaptive partitioning framework effectively reduces the size of the finite partition, which offers a considerable advantage over abstraction-based methods that use a uniform partition.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".