Geodesic
Asymptotics of the optimal time in a~singular perturbation linear problem
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 1, pp. 63-75

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A time-optimal control problem is considered for a linear system with fast and slow variables and smooth geometric constraints on the control. For the optimal time and optimal control, asymptotic expansions in a small parameter at the derivatives in the equations of the system and a small perturbation of the initial conditions are constructed.
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~singular perturbation linear problem. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 1, pp. 63-75. http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a6/