An optimal control framework for the climb and descent economy modes of flight management systems
Bibliographic record
Abstract
This paper proposes an optimal control framework for the climb and descent economy modes of a flight management system (FMS) yielding a solution that can be implemented in real-time flights below the drag divergence Mach number. The problem is formulated as the optimization of a functional that trades off the fuel- and time-related costs of a flight as a function of a (crew-supplied) parameter called the cost index. The work builds on previous research of the authors for the cruise phase and extends it to the climb and descent phases of flight. More specifically, for both climb and descent, it is found that suboptimal solutions can be obtained as the positive real roots of a fifth-degree polynomial lying inside the flight envelope, which can be found using fast-converging algorithms such as Newton's method. The main contributions of this work are threefold. First, the proposed method gives physical insight because there is an analytical expression for each coefficient of the polynomial. Second, this approach eliminates the need to have a performance database in the system, thus making its implementation faster in real-time. Third, the solution exhibits the same behavior of airborne FMS units as a function of the cost index, which is justified in this paper based on Bellman's principle of optimality. This justification is an important theoretical contribution of the paper. A validation of the approximate solution is obtained using the shooting method to compute the optimal trajectories and compare them against the proposed suboptimal solution. Simulation results show that, for an Airbus A320 model and for a Gulfstream-IV aircraft model, the relative error of the suboptimal trajectories when compared to the optimal trajectories is small for climb and descent trajectories, respectively.
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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 | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 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".