Geodesic
Barycentric method in the optimal control shape reflecting surface of the mirror antenna
Matematičeskoe modelirovanie, Tome 29 (2017) no. 11, pp. 140-150.

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In the article use barycentric method in the solution of the optimal control shape reflecting surface of the mirror antenna is proposed. The reflector is configured of a deformable membrane. The control problem to the solution in the approximation methods of Ritz and Galerkin biharmonic differential equation is reduced. With barycentric approximation method of Ritz for the whole region of analysis as a whole without its discretization into finite elements is defined. For a given approximation of the initial task of the Pontryagin maximum principle to the system of ordinary differential equations is reduced. It was proposed to solve this problem numerically using standard methods, such as Runge–Kutta. To determine the preference of the use barycentric the method of comparative examples of solution of optimal control problems form the reflecting surface of the reflector mirror antenna is considered. Additional positive properties barycentric method in relation to determining the number of control actions and their location on the control surfaces are highlighted.
Keywords: barycentric method, optimal control, membrane reflector mirror antenna, Pontryagin maximum principle. 
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I. S. Poljanskij. Barycentric method in the optimal control shape reflecting surface of the mirror antenna. Matematičeskoe modelirovanie, Tome 29 (2017) no. 11, pp. 140-150. http://geodesic.mathdoc.fr/item/MM_2017_29_11_a9/

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