Pontryagin's maximum principle of optimal control problems with time-delay
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 5, pp. 3-19.

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In this paper, we consider an optimal control problem with time-delay. The state and the control variables contain various constant time-delays. This allows us to represent the necessary conditions in an explicit form. Solution of this problem with infinite terminal time is also given.
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G. V. Bokov. Pontryagin's maximum principle of optimal control problems with time-delay. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 5, pp. 3-19. http://geodesic.mathdoc.fr/item/FPM_2009_15_5_a0/

[1] Alekseev V. M., Tikhomirov V. M., Fomin S. V., Optimalnoe upravlenie, Fizmatlit, M., 2005

[2] Arkhipov G. I., Sadovnichii V. A., Chubarikov V. N., Lektsii po matematicheskomu analizu, Drofa, M., 2003

[3] Matveev A. S., “Zadachi optimalnogo upravleniya s zapazdyvaniem obschego vida i fazovymi ogranicheniyami”, Izv. AN SSSR. Ser. mat., 52:6 (1988), 1200–1229 | MR | Zbl

[4] Myshkis A. D., Differentsialnye uravneniya s zapazdyvayuschim argumentom, Dis. $\dots$ dokt. fiz.-mat. nauk, Riga, 1949

[5] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1976

[6] Kharatishvili G. L., Optimalnye protsessy s zapazdyvaniem, Tbilisi, 1966

[7] Elsgolts L. E., Norkin S. B., Vvedenie v teoriyu differentsialnykh uravnenii s otklonyayuschimsya argumentom, M., 1971

[8] Bakke V. L., “Optimal fields of problems with delays”, J. Optim. Theory Appl., 33:1 (1981), 69–84 | DOI | MR | Zbl

[9] Chyung D. H., Lee E. B., “Linear optimal systems with time delays”, SIAM J. Control, 4:3 (1966), 548–575 | DOI | MR | Zbl

[10] Guinn T., “Reduction of delayed optimal control problems to nondelayed problems”, J. Optim. Theory Appl., 18:3 (1976), 371–377 | DOI | MR | Zbl

[11] Halanay A., “Optimal controls for systems with time lag”, SIAM J. Control, 6:2 (1968), 215–234 | DOI | MR | Zbl

[12] Hestenes M. R., “On variational theory and optimal control theory”, SIAM J. Control, 3:1 (1965), 23–48 | MR | Zbl