Article 1417

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Dikusar Vasily Vasilevich, doсtor of physical and mathematical sciences, professor, chief researcher of department of security and non-linear analysis, Federal Research Center for computer science and management » of the Russian Academy of Sciences (Computing center named after A. A. Dorodnitsyn of Russian Academy of Sciences) (119333, 40 Vavilov street, Moscow, Russia),
Koshka Marjan, doctor of physical and mathematical sciences, professor, head of sub-department of computer science and mathematics, Kazimierz Pulaski University of Technologies and Humanities, (26600, 29 Mal'chevskogo street, Radom, Poland), 
Figura Adam, doctor of physical and mathematical sciences, professor, dean of faculty of mathematics and Informatics, Kazimierz Pulaski University of Technologies and Humanities, (26600, 29 Mal'chevskogo street, Radom, Poland),

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This work presents a numerical study of optimal reentry body descent with constraints. The main purpose of optimization is to minimize the maximum surface temperature of the spacecraft. We consider the problem of choosing the angle of attack of the apparatus, which is retarded in the atmosphere while minimizing the total heat flux, taking into account the limitations on the total overload of the high-speed head. The problem is solved on the basis of the maximum principle (regular case), taking into account the restrictions on overload. Necessary conditions for an extremum are given in the irregular case when the optimal trajectory contains an interval. The degenerate maximum principle is regularized by changing the structure of the constraints. It is proved that the interaction of various methods is critical for the successful consideration of this problem with a lot of restrictions. The decrease in surface temperature is significant. In addition, the maximum heat flux and total heat flux can be significantly reduced by optimal choice of the trajectory. We propose a two-stage method for solving optimal control problems. In the first stage we determine the geometry of the optimal trajectory by use the discrete system of ordinary differential equations and solving the improper task of nonlinear programming of high dimension. The second step tests the validity of the maximum principle for the solutions obtained. To solve all problems we use methods of factor analysis, continuation of solutions on parameters,recovery dependencies, and the forecast for the next approximations. 

Key words

reliability, nonlinear programming, maximum principle, parallel computing, minimum of maximum heating

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Дата создания: 17.01.2018 09:43
Дата обновления: 17.01.2018 13:33