Albu, Alla; Zubov, Vladimir Optimal control for one complex dynamic system. I. (English) Zbl 1176.49004 Bul. Acad. Ştiinţe Repub. Mold., Mat. 2009, No. 1(59), 3-21 (2009). The optimal control problem of the metal solidification in casting is considered. The process is modeled by a three-dimensional two-phase initial-boundary value problem of the Stefan type. A numerical algorithm is presented for solving the direct problem. The optimal control problem as solved numerically using the gradient method. The gradient of the cost function was found with the help of the conjugate problem. The discrete conjugate problem was posed with the help of Fast Automatic Differentiation technique. Cited in 1 Review MSC: 49J20 Existence theories for optimal control problems involving partial differential equations 93C20 Control/observation systems governed by partial differential equations Keywords:heat conduction; Stefan problem; finite-difference scheme; optimal control; gradient method; fast automatic differentiation technique PDFBibTeX XMLCite \textit{A. Albu} and \textit{V. Zubov}, Bul. Acad. Științe Repub. Mold., Mat. 2009, No. 1(59), 3--21 (2009; Zbl 1176.49004)