Geodesic
A method of optimal real-time computation of a~linear system with retarded control
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 1, pp. 17-30

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A new method of solving time-optimal control problems in real time has been developed. The method is based on the following: 1) approximating the attainability sets with a family of hyperplanes; 2) subdividing the whole computational process into the computations performed beforehand and those that are carried out while the control takes place; 3) integrating differential equations only over the displacement intervals of the control completion moment and the switching moments. The labor-intensive characteristic of the method is evaluated. Characteristics of calculating the optimal control of a linear system with retarded control in real time are considered. The results of modeling and numerical estimations are presented. 
@article{SJVM_2014_17_1_a1,
     author = {V. M. Aleksandrov},
     title = {A method of optimal real-time computation of a~linear system with retarded control},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {17--30},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2014_17_1_a1/}
}
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V. M. Aleksandrov. A method of optimal real-time computation of a~linear system with retarded control. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 1, pp. 17-30. http://geodesic.mathdoc.fr/item/SJVM_2014_17_1_a1/