Demim, Fethi; Louadj, Kahina; Aidene, Mohamed; Nemra, Abdelkrim Minimization fuel rate of an aircraft. (English) Zbl 1431.49023 Far East J. Appl. Math. 98, No. 2, 73-82 (2018). Summary: The aim of the paper is to minimize the fuel rate of an aircraft. This problem is solved by shooting method coupled with a relaxation method based on Pontryagin principle. We use a shooting method to find the initial condition of adjoint state and illustrate results by using a numerical solution. MSC: 49K15 Optimality conditions for problems involving ordinary differential equations 49J45 Methods involving semicontinuity and convergence; relaxation Keywords:Pontryagin principle’s; optimal control; optimization; shooting method; relaxation method; fuel consumption rate; aircraft Software:Matlab × Cite Format Result Cite Review PDF Full Text: DOI References: [1] D. G. Hull, Optimal Control Theory for Applications, Springer-Verlag, New York, 2003. · Zbl 1113.49001 [2] J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970. · Zbl 0241.65046 [3] E. Trelat, Contrôle optimal: théorie et applications, Vuibert, collection Mathématiques Concrètes, France, 2005. · Zbl 1112.49001 [4] P. Hagelauer and F. Mora Camino, A Soft Dynamic Programming Approach for On-line Aircraft 4D-trajectory Optimization, LAAS, Toulouse, 2014. · Zbl 0943.90075 [5] Efstathios Bakolas-Panagiotis Tsiotras, Optimal synthesis of the Zermelo-MarkovDubins, Problem in a constant drift field, J. Optimal Theory Applications, Springer, 156 (2013), 469-492. · Zbl 1263.49048 [6] Suresh P. Sethi and Gerald L. Thompsonn, Optimal control theory, applications to management science and economics, second edition, 2000. · Zbl 0998.49002 [7] K. Louadj and F. Demim, Minimisation d’un débit énergétique d’un avion, Proceeding SMAI, Toulouse, 2016. [8] G. M. Baudet, Asynchronous iterative methods for multiprocesseurs, J. ACM 25 (1978), 226-244. · Zbl 0372.68015 [9] L. S. Pontriaguine, V. G. Boltyanski, R. V. Gamkrelidze and E. F. Mischenko, The Mathematical Theory of Optimal Processes, Interscience Publishers, New York, 1962. · Zbl 0102.32001 [10] S. Trrouche, P. Spiteri, F. Messine and M. Aidene, Optimal control of a large thermic process, Journal of Process Control 25 (2015), 50-58. [11] F. Kara, P. Spitéri, F. Messine and M. Aidene, A numerical optimal control method for solving a large thermic process, RAIRO Operations Research, EDP Sciences 50(2) (2016), 297-314. · Zbl 1338.49058 [12] Y. Park and Morton E. O’Kelly, Fuel burn rates of commercial passenger aircraft: Variations by seat configuration and stage, distance, Journal of Transport Geography 41 (2014), 137-147. [13] F. Demim, K. Louadj, M. Aidene and A. Nemra, Solution of an optimal control problem with vector control using relaxation method, Automatic Control and System Engineering Journal 16(2) (2016), ISSN 1687-4811, ICGST LLC, Delaware, USA, 2016. · Zbl 1429.49037 [14] K. Louadj, P. Spitéri, M. Aidene and F. Messine, An optimal control problem with free final time for aircraft flight with wind (regular paper), Colloque sur l’optimisation et les systèmes d’information (COSI 2014), Bejaia, 08/06/201410/06/2014. [15] K. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.