Geodesic
Asymptotic expansion of solution of one singularly perturbed optimal control problem with convex integral performance index and cheap control
Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 3, pp. 5-13.

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We consider the problem of optimal control for a linear system with constant coefficients with convex integral performance index contains small parameter in integral part in the class of piecewise continuous controls with a smooth control constraints. The article is based on asymptotic of the initial vector of the adjoint state, which determines the type of optimal control. In the time-optimal control problem limit problem has a solution with discontinuous control but the perturbed problem has continuous control. It is proved that in this case the solution is decomposed in an series with a complex structure. But optimal control is decomposed in a power series of expansion in small parameter in the cheap control problem.
Keywords: optimal control, cheap controls, asymptotic expansion, small parameter. . 
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A. R. Danilin; A. A. Shaburov. Asymptotic expansion of solution of one singularly perturbed optimal control problem with convex integral performance index and cheap control. Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 3, pp. 5-13. http://geodesic.mathdoc.fr/item/SJIM_2022_25_3_a0/

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