Geodesic
A complete asymptotic expansion of a solution to a singular perturbation optimal control problem on an interval with geometric constraints
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 52-60 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider an optimal control problem for solutions of a boundary value problem on an interval for a second-order ordinary differential equation with a small parameter at the second derivative. The control is scalar and satisfies geometric constraints. Expansions of a solution to this problem up to any power of the small parameter are constructed and validated.
Keywords: optimal control, asymptotic expansion, singular perturbation problems, small parameter. 
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A. R. Danilin. A complete asymptotic expansion of a solution to a singular perturbation optimal control problem on an interval with geometric constraints. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 52-60. http://geodesic.mathdoc.fr/item/TIMM_2016_22_1_a5/

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