Geodesic
A singular solution to the problem of minimizing resource consumption
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 1, pp. 5-18

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An iterative method of finding a singular solution to the problem of minimizing resource consumption has been developed. This method is based on the information about the finite control structure. A condition for existence of a singular solution is obtained. The limit value for transferring the time between the normal and the singular solutions is found. A relation between the variations of the control switching moments and the variations of the initial conditions of the adjoint system is determined. A system of linear algebraic equations relating the variations of the initial conditions of the adjoint system to the variations of the phase coordinates from a given final state of the system is obtained. The computational algorithm, the modeling results and the numerical calculations are presented. 
@article{SJVM_2016_19_1_a2,
     author = {V. M. Aleksandrov},
     title = {A singular solution to the problem of minimizing resource consumption},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {5--18},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2016_19_1_a2/}
}
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V. M. Aleksandrov. A singular solution to the problem of minimizing resource consumption. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 1, pp. 5-18. http://geodesic.mathdoc.fr/item/SJVM_2016_19_1_a2/