Geodesic
Optimal control problem for the impulsive differential equations with non-local boundary conditions
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2013), pp. 34-45

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The optimal control problem is investigated, where the state of the controlled system is described by the impulsive differential equations with non-local boundary conditions. The existence and uniqueness of the non-local impulsive boundary problem by fixed admissible controls are proved using the contraction mapping principle. The gradient of the functional is calculated under certain conditions on the initial data. The necessary conditions for optimality of the first order are obtained.
Keywords: non-local boundary conditions, impulsive systems, necessary conditions of optimality, gradient of functional, existence and uniqueness of the solution. 
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     author = {Ya. A. Sharifov},
     title = {Optimal control problem for the impulsive differential equations with non-local boundary conditions},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {34--45},
     publisher = {mathdoc},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2013_4_a2/}
}
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Ya. A. Sharifov. Optimal control problem for the impulsive differential equations with non-local boundary conditions. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2013), pp. 34-45. http://geodesic.mathdoc.fr/item/VSGTU_2013_4_a2/