Geodesic
Optimality conditions of the maximum principle type in bilinear control problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 12, pp. 2054-2064 Cet article a éte moissonné depuis la source Math-Net.Ru

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The optimization of a bilinear functional related to a linear state system with a modular control constraint is considered. Exact formulas for the functional increment are used to obtain sufficient conditions for the optimality of extremal controls that supplement the maximum principle. These conditions are represented in the form of inequalities and equalities for one-variable functions on a time interval. The optimization of a quadratic functional with the help of a matrix conjugate function is reduced to the bilinear case. 
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V. G. Antonik; V. A. Srochko. Optimality conditions of the maximum principle type in bilinear control problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 12, pp. 2054-2064. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a5/

[1] Arguchintsev A. V., Dykhta V. A., Srochko V. A., “Optimalnoe upravlenie: nelokalnye usloviya, vychislitelnye metody i variatsionnyi printsip maksimuma”, Izv. vyssh. uchebn. zavedenii. Matematika, 2009, no. 1, 3–43

[2] Srochko V. A., Iteratsionnye metody resheniya zadach optimalnogo upravleniya, Fizmatlit, M., 2000

[3] Baturin V. A., Urbanovich D. E., Priblizhennye metody optimalnogo upravleniya, osnovannye na printsipe rasshireniya, Nauka, Novosibirsk, 1997 | MR

[4] Strekalovskii A. S., Elementy nevypukloi optimizatsii, Nauka, SO, Novosibirsk, 2003

[5] Tyatyushkin A. I., Mnogometodnaya tekhnologiya optimizatsii upravlyaemykh sistem, Nauka, Novosibirsk, 2006

[6] Antipina N. V., Dykhta V. A., “Lineinye funktsii Lyapunova–Krotova i dostatochnye usloviya optimalnosti v forme printsipa maksimuma”, Izv. vyssh. uchebn. zavedenii. Matematika, 2002, no. 12, 11–22

[7] Dykhta V. A., “Analiz dostatochnykh uslovii optimalnosti s mnozhestvom funktsii tipa Lyapunova”, Tr. IMM UrO RAN, 16, no. 5, 2010, 66–75

[8] Nikolskii M. S., “O dostatochnosti printsipa maksimuma Pontryagina v nekotorykh optimizatsionnykh zadachakh”, Vestnik Mosk. un-ta. Ser. 15. Vychisl. matem. i kibern., 2005, no. 1, 35–43

[9] Srochko V. A., Antonik V. G., “Dostatochnye usloviya optimalnosti ekstremalnykh upravlenii na osnove formul prirascheniya funktsionala”, Izv. vyssh. uchebn. zavedenii. Matematika, 2014, no. 8, 96–102

[10] Aksenyushkina E. V., Srochko V. A., “Dostatochnye usloviya optimalnosti dlya odnogo klassa nevypuklykh zadach upravleniya”, Zh. vychisl. matem. i matem. fiz., 55:10 (2015), 1670–1680 | DOI | Zbl