On the optimal control of hybrid systems: analysis and zonal algorithms for trajectory and schedule optimization
Bibliographic record
Abstract
In [M.S. Shaikh, et al., 2002, April 2003, 2003] a class of hybrid optimal control problems was formulated and a set of necessary conditions for hybrid system trajectory optimally was presented. Employing these conditions, we presented and analyzed a class of general hybrid maximum principle (HMP) based algorithms for hybrid systems optimization. In this paper it is first shown how the HMP algorithm class can be extended with discrete search algorithms, which find locally optimal switching schedules and their associated, switching times. We then present the notion of optimality zones; these zones have a well defined geometrical structure and once they have been computed (or approximated) they permit the exponential complexity search for optimal schedule sequences of the first method to be reduced to a complexity level which under reasonable hypotheses is proportional to the number of zones. The algorithm HMP[Z] which performs this optimization is essentially a minor modification of the HMP algorithm and permits one to reach the global optimum in a single run of the HMP[MCS] algorithm. The efficacy of the proposed algorithms is illustrated via computational 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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".