Geodesic
Optimal control of impulsive systems with nonlocal boundary conditions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2013), pp. 75-84

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In this paper we study an optimal control problem, where states of a control system are described by impulsive differential equations with nonlocal boundary conditions. With the help of the contraction principle we prove the existence and uniqueness of a solution to the corresponding boundary value problem with fixed admissible controls. We calculate the first and second variations of the functional. Using the variation of controls, we establish various necessary optimality conditions of the second order.
Keywords: nonlocal boundary conditions, optimal control, impulsive systems, existence and uniqueness of solutions. 
@article{IVM_2013_2_a7,
     author = {Ya. A. Sharifov},
     title = {Optimal control of impulsive systems with nonlocal boundary conditions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {75--84},
     publisher = {mathdoc},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_2_a7/}
}
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Ya. A. Sharifov. Optimal control of impulsive systems with nonlocal boundary conditions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2013), pp. 75-84. http://geodesic.mathdoc.fr/item/IVM_2013_2_a7/