Geodesic
Asymptotics of the solution to a liner-quadratic periodic problem with a singular matrix perturbation in the performance index
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 4, pp. 603-616

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A liner-quadratic periodic optimal control problem with a singular matrix perturbation in the performance index is considered. An asymptotic expansion of its solution in nonnegative integer powers of is constructed by applying a direct scheme. The proximity of the exact solution to the approximate one is estimated for the control, trajectory, and functional. It is shown that the functional minimized does not increase when a higher order asymptotic approximation to the optimal control is used. 
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     title = {Asymptotics of the solution to a liner-quadratic periodic problem with a singular matrix perturbation in the performance index},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     number = {4},
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     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_4_a4/}
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G. A. Kurina; S. S. Shchekunskikh. Asymptotics of the solution to a liner-quadratic periodic problem with a singular matrix perturbation in the performance index. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 4, pp. 603-616. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_4_a4/