Email this article Constraints in the Problem of Calculating Optimal Trajectories for a Supersonic Non-Maneuverable Aircraft
- Authors: Kumakshev S.A.1, Shmatkov A.M.1
-
Affiliations:
- Institute for Problems in Mechanics of the RAS
- Issue: Vol 87, No 4 (2023)
- Pages: 631-641
- Section: Articles
- URL: https://journals.rcsi.science/0032-8235/article/view/138883
- DOI: https://doi.org/10.31857/S0032823523040070
- EDN: https://elibrary.ru/WIGEBL
- ID: 138883
Cite item
Open Access
Access granted
Subscription Access
Abstract
The influence of phase and other constraints on the method of searching for the trajectories of the movement of a civil supersonic aircraft, which are optimal in terms of fuel consumption, is considered. Based on the solutions found by the dynamic programming method, taking into account numerous restrictions on flight altitude, pitch angle, normal high-speed overload, aircraft speed, engine thrust, etc., it is shown that almost all of these conditions can be ignored during the initial stage of calculations, since the optimal solution does not reach them. Therefore, one can first apply the maximum principle, and use the dynamic programming method only in those cases where a substantial part of the constraints turns out to be significant.
About the authors
S. A. Kumakshev
Institute for Problems in Mechanics of the RAS
Author for correspondence.
Email: kumak@ipmnet.ru
Russia, Moscow
A. M. Shmatkov
Institute for Problems in Mechanics of the RAS
Email: kumak@ipmnet.ru
Russia, Moscow
References
- Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V., Mishchenko E.F. The Mathematical Theory of Optimal Processes. N.Y.: Wiley, 1963.
- Bellman R. Dynamic Programming. Princeton: Univ. Press, 1957.
- Rosenow J., Strunck D., Fricke H. Trajectory Optimization in Daily Operations // CEAS Aeronaut. J., 2020, vol. 11, pp. 333–343.
- Murrieta-Mendoza A., Botez R.M. Methodology for vertical-navigation flight-trajectory cost calculation using a performance database // J. Aerosp. Inf. Syst., 2015, vol. 12, no. 8, pp. 519–532.
- Alligier R. Predictive distribution of mass and speed profile to improve aircraft climb prediction // J. Air Transp., 2020, vol. 28, no. 3, pp. 114–123.
- Franco A., Rivas D. Optimization of multiphase aircraft trajectories using hybrid optimal control // J. Guid. Control Dyn., 2015, vol. 38, no. 3, pp. 452–467.
- Murrieta-Mendoza A., Romain C., Botez R.M. 3D cruise trajectory optimization inspired by a shortest path algorithm // Aerospace, 2020, no. 7, pp. 99–119.
- Soler M., Olivares A., Staffetti E. Multiphase optimal control framework for commercial aircraft four-dimensional flight-planning problems // J. Aircr., 2015, vol. 52, no. 1, pp. 274–286.
- Garca-Heras J., Soler M., Saez F.J. Collocation methods to minimum-fuel trajectory problems with required time of arrival in ATM // J. Aerosp. Inf. Syst., 2016, vol. 13, no. 7, pp. 243–265.
- Langelaan J.W. Long distance/duration trajectory optimization for small UAVs // in: AIAA Guidance, Navigation and Control Conf. South Carolina: Hilton Head, 2007, pp. 3654–3667.
- Rosenow J., Lindner M., Scheiderer J. Advanced flight planning and the benefit of in-flight aircraft trajectory optimization // Sustainability, 2021, vol. 13, no. 3, pp. 1383–1401.
- Kumakshev S.A., Shmatkov A.M. Optimal fuel consumption trajectories of a civil supersonic aircraft // J. Comput. Syst. Sci. Int., 2022, vol. 61, no. 4, pp. 664–676.
- Rosenow J., Förster S., Lindner M., Fricke H. Multi-objective trajectory optimization // Int. Transp., 2016, vol. 68, no. 1, pp. 40–43.
- Kumakshev S.A., Shmatkov A.M. Flight trajectory optimization without decomposition into separate stages // IOP Conf. Ser. Mater. Sci. Eng., 2018, vol. 468, no. 012033.
- Bochkarev A.F., Andreevsky V.V., Belokonov V.M. et al. Aircraft Aeromechanics: Flight Dynamics. Moscow: Mashinostroenie, 1985. (in Russian)
- Grevtsov N.M., Kumakshev S.A., Shmatkov A.M. Optimization of the flight trajectory of a non-manoeuvrable aircraft to minimize fuel consumption by the dynamic programming method // JAMM, 2017, vol. 81, iss. 5, pp. 368–374.
- Zhelnin Yu.N., Utemov A.E., Shmatkov A.M. Minimum time loop maneuver with no speed loss // J. Comput. Syst. Sci. Int., 2022, vol. 51, no. 6, pp. 833–848.
Supplementary files
