Geodesic
Asymptotics of Optimal Synthesis for One Class of Extremal Problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations. Certain mathematical problems of optimal control, Tome 233 (2001), pp. 95-124.

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

The asymptotics of an optimal control while approaching the origin is found for a class of mean square deviation minimization problems with a unilateral force. The asymptotics is described by a series of impulses of maximal amplitude that decrease in time and have the support in the neighborhoods of points of a certain infinite arithmetic progression. The results are applied to the investigation of controlled populational dynamics described by the Lottka–Volterra–Kolmogorov equations. 
@article{TM_2001_233_a3,
     author = {M. I. Zelikin and L. F. Zelikina and R. Hildebrand},
     title = {Asymptotics of {Optimal} {Synthesis} for {One} {Class} of {Extremal} {Problems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {95--124},
     publisher = {mathdoc},
     volume = {233},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2001_233_a3/}
}
TY  - JOUR
AU  - M. I. Zelikin
AU  - L. F. Zelikina
AU  - R. Hildebrand
TI  - Asymptotics of Optimal Synthesis for One Class of Extremal Problems
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2001
SP  - 95
EP  - 124
VL  - 233
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2001_233_a3/
LA  - ru
ID  - TM_2001_233_a3
ER  - 
%0 Journal Article
%A M. I. Zelikin
%A L. F. Zelikina
%A R. Hildebrand
%T Asymptotics of Optimal Synthesis for One Class of Extremal Problems
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2001
%P 95-124
%V 233
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2001_233_a3/
%G ru
%F TM_2001_233_a3
M. I. Zelikin; L. F. Zelikina; R. Hildebrand. Asymptotics of Optimal Synthesis for One Class of Extremal Problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations. Certain mathematical problems of optimal control, Tome 233 (2001), pp. 95-124. http://geodesic.mathdoc.fr/item/TM_2001_233_a3/

[1] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1969

[2] Fuller A. T., “Constant-ratio trajectories in optimal control systems”, Intern. J. Contr., 58:6 (1993), 1409–1435 | DOI | MR | Zbl

[3] Kelley H. J., Kopp R. E., Moyer M. G., “Singular extremals”, Topics in optimization, Acad. Press, N.Y., 1967, 63–101 | MR

[4] Nitecki Z., Differentiable dynamics, MIT Press, Cambridge, MA, 1971 | MR

[5] Zelikin M. I., Borisov V. F., Theory of chattering control: With applications to astronautics, robotics, economics and engineering, Syst. Contr.: Found. Appl., Birkhäuser, Boston etc., 1994 | MR | Zbl