Geodesic
Asymptotics of the optimal time in a time-optimal problem with two small parameters
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 92-99 Cet article a éte moissonné depuis la source Math-Net.Ru

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A time-optimal problem of control of a small-mass point by a force of bounded magnitude in a nonresisting medium is considered. An asymptotic expansion of the optimal time and optimal control is constructed with respect to two independent small parameters: the mass of the point and the perturbation of the initial conditions. It is shown that the asymptotics of the optimal time in this problem is complicated even for cases of general position.
Keywords: optimal control, time-optimal control problem, asymptotic expansion, singular perturbation problems, small parameter. 
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A. R. Danilin; O. O. Kovrizhnykh. Asymptotics of the optimal time in a time-optimal problem with two small parameters. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 92-99. http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a8/

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