Computing Viable Sets and Reachable Sets to Design Feedback Linearizing Control Laws Under Saturation
Why this work is in the frame
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Bibliographic record
Abstract
We consider feedback linearizable systems subject to bounded control input and nonlinear state constraints. In a single computation, we synthesize 1) parameterized nonlinear controllers based on feedback linearization, and 2) the set of states over which this controller is valid. This is accomplished through a reachability calculation, in which the state is extended to incorporate input parameters. While we use a Hamilton-Jacobi formulation, a viability approach is also feasible. The result provides a mathematical guarantee that for all states within the computed set, there exists a control law that simultaneously satisfy two separate goals: envelope protection (no violation of state constraints), and stabilization despite saturation. We apply this technique to two real-world systems: the longitudinal dynamics of a civil jet aircraft, and a two-aircraft, planar collision avoidance scenario. The result, in both cases, is a feasible range of input parameters for the nonlinear control law, and a corresponding controlled invariant set
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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 | 0.000 | 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 |
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 it