Geodesic
Asymptotics of the optimal control in a~linear optimal control problem
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 2, pp. 186-198

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An optimal control problem is considered with fast and slow variables, smooth geometric constraints on the control, and a terminal performance criterion. The connection is shown between the optimal control and a solution of a certain nonlinear system of algebraic equations for the vector of the initial conditions of conjugate variables in the maximum principle. Based on this connection and the known results on the asymptotics of a solution.
Keywords: optimal control, terminal performance criterion, bounded controls, asymptotic expansions.
Mots-clés : singular perturbations 
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     author = {Yu. V. Parysheva},
     title = {Asymptotics of the optimal control in a~linear optimal control problem},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {186--198},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2010_16_2_a16/}
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Yu. V. Parysheva. Asymptotics of the optimal control in a~linear optimal control problem. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 2, pp. 186-198. http://geodesic.mathdoc.fr/item/TIMM_2010_16_2_a16/