Optimal Control Framework for Cruise Economy Mode of Flight Management Systems
Bibliographic record
Abstract
The main contribution of this paper is to propose optimal and suboptimal control solutions to the cruise economy mode problem in a flight management system for flights below the drag divergence Mach number. The problem is formulated as an optimization of a functional that trades off the fuel and time-related costs of a flight using a (crew-supplied) cost index CI. A novel approach is proposed based on solving the problem analytically using a combination of Pontryagin’s maximum principle and the Hamilton–Jacobi–Bellman equation. A suboptimal analytical solution for the true airspeed is obtained in state feedback form, which reduces to the well-known optimal solution for maximum range when the cost index vanishes. An analytical solution for the speed target as a function of the cost index gives physical insight, allows one to analytically compute sensitivities, and eliminates the need to have a performance database to store the optimal speed schedules in the system. An extension shows that the approach is valid when the aircraft is turning with a small bank angle. Overall, this work provides not only a very efficient means of implementing the optimal speed schedules in an onboard flight management system for flights below the divergence Mach number, but also extends the theory of aircraft performance to the more general case based on a nonzero cost index. The new results are compared with flight simulation data for an A320 Airbus aircraft.
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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 | 0.001 |
| 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 | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".