Geodesic
Investigation of some control models
Trudy Instituta matematiki i mehaniki, Control, stability, and inverse problems of dynamics, Tome 12 (2006) no. 2, pp. 142-151 
M. S. Nikol'skii. Investigation of some control models. Trudy Instituta matematiki i mehaniki, Control, stability, and inverse problems of dynamics, Tome 12 (2006) no. 2, pp. 142-151. http://geodesic.mathdoc.fr/item/TIMM_2006_12_2_a12/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Three simplified models of quarrying are considered. The first and third models are extremal, and the second is described in terms of a differential game. For each of the models, sufficient conditions on the parameters of the problem are obtained that guarantee a simple form of the optimal control. Pontrayagin's maximum principle and the theory of positional differential games, elaborated by N. N. Krasovskii and his school, are used.

[1] Avvakumov S. N., Kiselev Yu. N., Orlov M. V., “Issledovanie odnomernoi optimizatsionnoi modeli MD1. Beskonechnyi gorizont. Konechnyi gorizont”, Problemy dinamicheskogo upravleniya, Cb. nauchn. tr. Vyp. 1, Izd-vo MGU, M., 2005, 111–136 | MR

[2] Grigorenko N. L., Kamzolkin D. V., Lukyanova L. N., “Reshenie odnoi zadachi optimalnogo upravleniya”, Problemy dinamicheskogo upravleniya, Cb. nauchn. tr. Vyp. 1, Izd-vo MGU, M., 2005, 137–144 | MR

[3] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1983 | MR | Zbl

[4] Li E. B., Markus L., Osnovy teorii optimalnogo upravleniya, Nauka, M., 1972 | MR

[5] Vasilev F. P., Metody optimizatsii, Faktorial Press, M., 2002

[6] Nikolskii S. M., Kurs matematicheskogo analiza, T. 2, Nauka, M., 1991 | MR

[7] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1974 | MR | Zbl

[8] Shiryaev A. N., Veroyatnost, Nauka, M., 1980 | MR | Zbl