Geodesic
On the theory of singular optimal controls in dynamic systems with control delay
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 5, pp. 747-767

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An optimal control problem with a control delay is considered, and a more broad class of singular (in classical sense) controls is investigated. Various sequences of necessary conditions for the optimality of singular controls in recurrent form are obtained. These optimality conditions include analogues of the Kelley, Kopp–Moyer, R. Gabasov, and equality-type conditions. In the proof of the main results, the variation of the control is defined using Legendre polynomials. 
@article{ZVMMF_2017_57_5_a0,
     author = {M. D. Mardanov and T. K. Melikov},
     title = {On the theory of singular optimal controls in dynamic systems with control delay},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {747--767},
     publisher = {mathdoc},
     volume = {57},
     number = {5},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_5_a0/}
}
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M. D. Mardanov; T. K. Melikov. On the theory of singular optimal controls in dynamic systems with control delay. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 5, pp. 747-767. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_5_a0/