Geodesic
Investigation of a linear optimal control problem with state constraints
Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 1, pp. 3-9

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The optimal synthesis for specied linear optimal control problem with state constraints is found by using the Pontryagin maximum principle. 
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A. V. Arutyunov; D. A. Zhukov. Investigation of a linear optimal control problem with state constraints. Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 1, pp. 3-9. http://geodesic.mathdoc.fr/item/VMJ_2010_12_1_a0/