Constraints in the Problem of Finding Optimal Trajectories for a Supersonic Non-Maneuverable Aircraft
The influence of phase and other constraints on the method of searching for the trajectories of a civil supersonic aircraft that are optimal in terms of fuel consumption is considered. Based on the solutions found by the dynamic programming method, which take into account the numerous conditions tha...
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| Vydáno v: | Mechanics of solids Ročník 58; číslo 7; s. 2586 - 2594 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Moscow
Pleiades Publishing
01.12.2023
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| ISSN: | 0025-6544, 1934-7936 |
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| Abstract | The influence of phase and other constraints on the method of searching for the trajectories of a civil supersonic aircraft that are optimal in terms of fuel consumption is considered. Based on the solutions found by the dynamic programming method, which take into account the numerous conditions that must be satisfied by the flight altitude, pitch angle, normal 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 these constraints do not affect the optimal solutions. Therefore, one can first apply the maximum principle and use the dynamic programming method only in those cases where a sizeable part of the constraints turns out to be significant. |
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| AbstractList | The influence of phase and other constraints on the method of searching for the trajectories of a civil supersonic aircraft that are optimal in terms of fuel consumption is considered. Based on the solutions found by the dynamic programming method, which take into account the numerous conditions that must be satisfied by the flight altitude, pitch angle, normal 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 these constraints do not affect the optimal solutions. Therefore, one can first apply the maximum principle and use the dynamic programming method only in those cases where a sizeable part of the constraints turns out to be significant. |
| Author | Kumakshev, S. A. Shmatkov, A. M. |
| Author_xml | – sequence: 1 givenname: S. A. surname: Kumakshev fullname: Kumakshev, S. A. email: kumak@ipmnet.ru organization: Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences (IPMech RAS) – sequence: 2 givenname: A. M. surname: Shmatkov fullname: Shmatkov, A. M. organization: Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences (IPMech RAS) |
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| Cites_doi | 10.1016/j.jappmathmech.2018.03.004 10.2514/1.D0181 10.2514/1.I010401 10.1134/S1064230712060160 10.2514/1.G000688 10.3390/su13031383 10.2514/1.C032697 10.1134/S1064230722040128 10.2514/1.I010347 10.1088/1757-899X/468/1/012033 10.3390/aerospace7070099 10.1007/s13272-019-00429-7 10.2514/6.2007-6737 |
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| Copyright | Allerton Press, Inc. 2023. ISSN 0025-6544, Mechanics of Solids, 2023, Vol. 58, No. 7, pp. 2586–2594. © Allerton Press, Inc., 2023. Russian Text © The Author(s), 2023, published in Prikladnaya Matematika i Mekhanika, 2023, Vol. 87, No. 4, pp. 631–641. |
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| Keywords | optimal trajectory maximum principle dynamic programming method supersonic aircraft phase constraint |
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| References_xml | – reference: AlligierR.Predictive distribution of mass and speed profile to improve aircraft climb predictionJ. Air Transp.20202811412310.2514/1.D0181 – reference: RosenowJ.FörsterS.LindnerM.FrickeH.Multi-objective trajectory optimizationInt. Transp.2016684043 – reference: PontryaginL. S.BoltyanskiiV. G.GamkrelidzeR. V.MishchenkoE. F.The Mathematical Theory of Optimal Processes1963New YorkWiley – reference: Garca-HerasJ.SolerM.SaezF. J.Collocation methods to minimum-fuel trajectory problems with required time of arrival in ATMJ. Aerospace Inf. Syst.20161324326510.2514/1.I010401 – reference: GrevtsovN. M.KumakshevS. A.ShmatkovA. M.Optimization of the flight trajectory of a non-manoeuvrable aircraft to minimize fuel consumption by thedynamic programming methodJ. Appl. Math. Mech.201781368374381392110.1016/j.jappmathmech.2018.03.004 – reference: SolerM.OlivaresA.StaffettiE.Multiphase optimal control framework for commercial aircraft four-dimensional flight-planning problemsJ. Aircraft20155227428610.2514/1.C032697 – reference: S. A. Kumakshev and A. M. Shmatkov, “Flight trajectory optimization qithout decomposition into separate stages,” IOP Conf. Ser. Mater. Sci. Eng. 468, 012033 (2018). – reference: A. Murrieta-Mendoza, C. Romain, and R. M. Botez, “3D cruise trajectory optimization inspired by a shortest path algorithm,” Aerospace, No. 7, 99–119 (2020). – reference: RosenowJ.LindnerM.ScheidererJ.Advanced flight planning and the benefit of in-flight aircraft trajectory optimizationSustainability2021131383140110.3390/su13031383 – reference: Murrieta-MendozaA.BotezR. M.Methodology for vertical-navigation flight-trajectory cost calculation using a performance databaseJ. Aerospace Inf. Syst.20151251953210.2514/1.I010347 – reference: J. W. Langelaan, “Long distance/duration trajectory optimization for small UAVs,” in Proc. AIAA Guidance, Navigation and Control Conf. (Hilton Head, 2007), pp. 3654–3667. – reference: BochkarevA. F.AndreevskyV. V.BelokonovV. M.Aircraft Aeromechanics: Flight Dynamics1985MoscowMashinostroenie – reference: BellmanR.Dynamic Programming1957PrincetonUniv. Press – reference: KumakshevS. A.ShmatkovA. M.Optimal fuel consumption trajectories of a civil supersonic aircraftJ. Comput. Syst. Sci. Int.202261664676447319710.1134/S1064230722040128 – reference: FrancoA.RivasD.Optimization of multiphase aircraft trajectories using hybrid optimal controlJ. Guid. Control Dyn.2015384524672015JGCD...38..452F10.2514/1.G000688 – reference: ZhelninYu. N.UtemovA. E.ShmatkovA. M.Minimum time loop maneuver with no speed lossJ. Comput. Syst. Sci. Int.201251833848308677810.1134/S1064230712060160 – reference: RosenowJ.StrunckD.FrickeH.Trajectory optimization in daily operationsCEAS Aeronaut. J.20201133334310.1007/s13272-019-00429-7 – volume: 81 start-page: 368 year: 2017 ident: 8679_CR16 publication-title: J. Appl. Math. Mech. doi: 10.1016/j.jappmathmech.2018.03.004 – volume: 28 start-page: 114 year: 2020 ident: 8679_CR5 publication-title: J. Air Transp. doi: 10.2514/1.D0181 – volume: 13 start-page: 243 year: 2016 ident: 8679_CR9 publication-title: J. Aerospace Inf. Syst. doi: 10.2514/1.I010401 – volume: 51 start-page: 833 year: 2012 ident: 8679_CR17 publication-title: J. Comput. Syst. Sci. Int. doi: 10.1134/S1064230712060160 – volume: 38 start-page: 452 year: 2015 ident: 8679_CR6 publication-title: J. Guid. Control Dyn. doi: 10.2514/1.G000688 – volume: 68 start-page: 40 year: 2016 ident: 8679_CR13 publication-title: Int. Transp. – volume-title: Aircraft Aeromechanics: Flight Dynamics year: 1985 ident: 8679_CR15 – volume: 13 start-page: 1383 year: 2021 ident: 8679_CR11 publication-title: Sustainability doi: 10.3390/su13031383 – volume: 52 start-page: 274 year: 2015 ident: 8679_CR8 publication-title: J. Aircraft doi: 10.2514/1.C032697 – volume: 61 start-page: 664 year: 2022 ident: 8679_CR12 publication-title: J. Comput. Syst. Sci. Int. doi: 10.1134/S1064230722040128 – volume-title: Dynamic Programming year: 1957 ident: 8679_CR2 – volume: 12 start-page: 519 year: 2015 ident: 8679_CR4 publication-title: J. Aerospace Inf. Syst. doi: 10.2514/1.I010347 – volume-title: The Mathematical Theory of Optimal Processes year: 1963 ident: 8679_CR1 – ident: 8679_CR14 doi: 10.1088/1757-899X/468/1/012033 – ident: 8679_CR7 doi: 10.3390/aerospace7070099 – volume: 11 start-page: 333 year: 2020 ident: 8679_CR3 publication-title: CEAS Aeronaut. J. doi: 10.1007/s13272-019-00429-7 – ident: 8679_CR10 doi: 10.2514/6.2007-6737 |
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| Title | Constraints in the Problem of Finding Optimal Trajectories for a Supersonic Non-Maneuverable Aircraft |
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