Geodesic
Asymptotic estimates for a solution of a singular perturbation optimal control problem on a closed interval under geometric constraints
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 104-112 Cet article a éte moissonné depuis la source Math-Net.Ru

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An optimal control problem is considered for solutions of a boundary value problem for a second-order ordinary differential equation on a closed interval with a small parameter at the second derivative. The control is scalar and satisfies geometric constraints. General theorems on approximation are obtained. Two leading terms of an asymptotic expansion of the solution are constructed and an error estimate is obtained for these approximations.
Keywords: optimal control, time-optimal problem, asymptotic expansion, singular perturbation problems, small parameter. 
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A. R. Danilin; N. S. Korobitsyna. Asymptotic estimates for a solution of a singular perturbation optimal control problem on a closed interval under geometric constraints. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 104-112. http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a9/

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