Geodesic
Using Galerkin Method for Solving Linear Optimal Control Problems
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 3, pp. 340-349.

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The linear optimal control problem is considered. Duration of the controlled process is fixed. It is necessary to minimize the functional, that characterizes the energy consumption. A method of constructing an approximate solution based on the Galerkin method is proposed. Examples of numerical solutions of the problem are given. 
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I. A. Pankratov. Using Galerkin Method for Solving Linear Optimal Control Problems. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 3, pp. 340-349. http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a14/

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