Geodesic
Investigation of the optimal control problem for metal solidification in a new formulation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 5, pp. 734-745 
A. F. Albu; V. I. Zubov. Investigation of the optimal control problem for metal solidification in a new formulation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 5, pp. 734-745. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_5_a2/
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     title = {Investigation of the optimal control problem for metal solidification in a new formulation},
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Voir la notice de l'article provenant de la source Math-Net.Ru

New formulations of the optimal control problem for metal solidification in a furnace are proposed and studied. The underlying mathematical model of the process is based on a three-dimensional two-phase initial-boundary value problem of the Stefan type. The formulated problems are solved numerically with the help of gradient optimization methods. The gradient of the cost function is computed by applying the fast automatic differentiation technique, which yields the exact value of the cost function gradient for a chosen discrete version of the optimal control problem. The research results are described and analyzed. Some of the results are illustrated.

[1] Albu A. F., Zubov V. I., “Matematicheskoe modelirovanie i issledovanie protsessa kristallizatsii metalla v liteinom dele”, Zh. vychisl. matem. i matem. fiz., 47:5 (2007), 882–902 | MR

[2] Albu A. F., Zubov V. I., “Ob optimalnom upravlenii protsessom kristallizatsii metalla v liteinom dele”, Zh. vychisl. matem. i matem. fiz., 48:5 (2008), 851–862 | MR

[3] Albu A. F., Zubov V. I., “Vychislenie gradienta funktsionala v odnoi zadache optimalnogo upravleniya, svyazannoi s kristallizatsiei metalla”, Zh. vychisl. matem. i matem. fiz., 49:1 (2009), 51–75 | MR

[4] Albu A. V., Zubov V. I., “O vybore funktsionala i raznostnoi skhemy pri reshenii zadachi optimalnogo upravleniya protsessom kristallizatsii metalla”, Zh. vychisl. matem. i matem. fiz., 51:1 (2011), 24–38 | MR

[5] Albu A. V., Albu A. F., Zubov V. I., “Vychislenie gradienta funktsionala v odnoi zadache optimalnogo upravleniya slozhnoi dinamicheskoi sistemoi”, Zh. vychisl. matem. i matem. fiz., 51:5 (2011), 814–833 | MR

[6] Albu A. V., Albu A. F., Zubov V. I., “Upravlenie protsessom kristallizatsii veschestva v liteinoi forme slozhnoi geometrii”, Zh. vychisl. matem. i matem. fiz., 52:12 (2012), 2149–2162

[7] Albu A. F., Zubov V. I., “O vliyanii parametrov ustanovki na upravlenie protsessom kristallizatsii veschestva v liteinom dele”, Zh. vychisl. matem. i matem. fiz., 53:2 (2013), 238–248 | DOI

[8] Albu A., Zubov V., “On the controlling of liquid metal solidification in foundry practice”, Operations Research Proc. 2011, Selected Papers of the International Conference on Operations Research (OR 2011) (August 30–September 2, 2011, Zurich, Switzerland), eds. D. Klatte, H.-J. Lüthi, K. Schmedders, Springer-Verlag, Berlin–Heidelberg, 2012, 3–8 | DOI

[9] Albu A. V., Zubov V. I., “O vizualnoi podderzhke reshenii zadach upravleniya slozhnymi dinamicheskimi sistemami”, Optimizatsiya i prilozheniya, VTs RAN, M., 2010, 33–41

[10] Evtushenko Y. G., “Computation of exact gradients in distributed dynamic systems”, Optimizat. Meth. and Software, 1998, no. 9, 45–75 | DOI | MR