Geodesic
On some problems of optimal control
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1383-1409

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A general method of computing optimal control for consumption of resources is developed. The method includes both normal and singular solution. According to the method the problem is subdivided into two independent tasks: 1) computation of the structure of optimal control; 2) computation of the switching moments of optimal control. The structure computation is based on the original method of constructing quasi-optimal control. And the control switching moments computes with the help of the relation found between the displacements of the initial conditions of the adjoint system and the displacements of the phase trajectory at the completion moment. Given the method of assignment of initial approximation. An iterative algorithm is developed, its characteristics being considered. The influence of system parameters and time of transfer on the structure of optimal control. The results of modeling and numerical computations are given.
Keywords: optimal control, speed, moving time, resource consumption, switching moments, iterative process, adjoint system, phase trajectory. 
@article{SEMR_2018_15_a106,
     author = {V. M. Aleksandrov},
     title = {On some problems of optimal control},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1383--1409},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a106/}
}
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V. M. Aleksandrov. On some problems of optimal control. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1383-1409. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a106/