Geodesic
Asymptotic solution of singularly perturbed linear-quadratic optimal control problems with discontinuous coefficients
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 4, pp. 628-652

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An asymptotic solution of a singularly perturbed linear-quadratic optimal control problem with discontinuous coefficients is constructed by directly substituting an boundary-layer asymptotic expansion of the solution into the condition of the problem and considering a series of problems for finding the asymptotic terms. The error in the approximate solution is estimated. It is shown that the values of the minimized functional do not increase when the next approximations of the optimal control are used. 
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     author = {G. A. Kurina and Nguy\^en Thị Ho\`ai},
     title = {Asymptotic solution of singularly perturbed linear-quadratic optimal control problems with discontinuous coefficients},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {628--652},
     publisher = {mathdoc},
     volume = {52},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_4_a4/}
}
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G. A. Kurina; Nguyên Thị Hoài. Asymptotic solution of singularly perturbed linear-quadratic optimal control problems with discontinuous coefficients. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 4, pp. 628-652. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_4_a4/