Geodesic
On a~construction of approximations for the optimal control in quasi-linear partial differential equations of the first order
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 6 (2014) no. 3, pp. 105-119.

Voir la notice de l'article provenant de la source Math-Net.Ru

We propose an approximate method of studying the optimal control problem for a quasilinear partial differential equations of first order. We consider the control bounded by a constant and quadratic criterion type. For each set of given coordinates and controls the Cauchy problem is reduced to an integral equation. It is considered the case when all the variables are integer values. The integral equation is replaced by the discrete analog. The existence and uniqueness of solution of this equation is proven. We use the method of successive approximations combined with the method of compressing maps.
Keywords: optimal control, quasilinear equation, nonlinear integral equation, discrete analog, method of compressing mapping. 
@article{MGTA_2014_6_3_a5,
     author = {Tursun K. Yuldashev},
     title = {On a~construction of approximations for the optimal control in quasi-linear partial differential equations of the first order},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {105--119},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2014_6_3_a5/}
}
TY  - JOUR
AU  - Tursun K. Yuldashev
TI  - On a~construction of approximations for the optimal control in quasi-linear partial differential equations of the first order
JO  - Matematičeskaâ teoriâ igr i eë priloženiâ
PY  - 2014
SP  - 105
EP  - 119
VL  - 6
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MGTA_2014_6_3_a5/
LA  - ru
ID  - MGTA_2014_6_3_a5
ER  - 
%0 Journal Article
%A Tursun K. Yuldashev
%T On a~construction of approximations for the optimal control in quasi-linear partial differential equations of the first order
%J Matematičeskaâ teoriâ igr i eë priloženiâ
%D 2014
%P 105-119
%V 6
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MGTA_2014_6_3_a5/
%G ru
%F MGTA_2014_6_3_a5
Tursun K. Yuldashev. On a~construction of approximations for the optimal control in quasi-linear partial differential equations of the first order. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 6 (2014) no. 3, pp. 105-119. http://geodesic.mathdoc.fr/item/MGTA_2014_6_3_a5/

[1] Butkovskii A. G., Teoriya optimalnogo upravleniya sistemami s raspredelennymi parametrami, Nauka, M., 1965 | MR

[2] Evtushenko Yu. G., Metody resheniya ekstremalnykh zadach i ikh primenenie v sistemakh optimizatsii, Nauka, M., 1982 | MR | Zbl

[3] Zaitsev V. F., Polyanin A. D., Spravochnik po differentsialnym uravneniyam s chastnymi proizvodnymi pervogo poryadka, Fizmatlit, M., 2003 | Zbl

[4] Rapoport E. Ya., Optimalnoe upravlenie sistemami s raspredelennymi parametrami, Vysshaya shkola, M., 2009

[5] Srochko V. A., Iteratsionnye metody resheniya zadach optimalnogo upravleniya, Fizmatlit, M., 2000

[6] Fedorenko R. P., Priblizhennoe reshenie zadach optimalnogo upravleniya, Nauka, M., 1978 | MR | Zbl

[7] Yuldashev T. K., “On a nonlinear system of functional difference equations with nonlinear complicated mixed maxima”, Advanced studies in contemporary mathematics, 13:1 (2006), 1–5 | MR

[8] Yuldashev T. K., “On a summery equation with weak nonlinear right-hand side”, Advanced studies in contemporary mathematics, 15:1 (2007), 95–98 | MR | Zbl

[9] Yuldashev T. K., “On a solvability of nonlinear summary equation of the third kind”, Proc. of Jangjeon Math. Soc., 16:1 (2013), 151–155 | MR | Zbl