Geodesic
Sufficient Optimality Conditions Based on Functional Increment Formulas in Control Problems
The Bulletin of Irkutsk State University. Series Mathematics, Tome 8 (2014), pp. 125-140 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A typical optimal control problem with convex terminal function is considered. Sufficient optimality conditions are obtained with the help non-standard functional increment formulas. So far, these formulas didn't apply to construction of numerical methods for successive improvement of auxiliary controls. A notion of strongly extremal control is introduced for each formula. It provides the maximum for Pontryagin's function in regard to some set of trajectories. Strongly extremal controls are optimal ones in linear and quadratic problems. In common case optimality of strongly extremal controls is provided with concavity condition of Pontryagin's function with regard phase variables. Examples of effective realization obtained relations are given.
Keywords: optimal control problem; the maximum principle; sufficient optimality conditions. 
@article{IIGUM_2014_8_a9,
     author = {V. A. Srochko and V. G. Antonik and E. V. Aksenyushkina},
     title = {Sufficient {Optimality} {Conditions} {Based} on {Functional} {Increment} {Formulas} in {Control} {Problems}},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {125--140},
     year = {2014},
     volume = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2014_8_a9/}
}
TY  - JOUR
AU  - V. A. Srochko
AU  - V. G. Antonik
AU  - E. V. Aksenyushkina
TI  - Sufficient Optimality Conditions Based on Functional Increment Formulas in Control Problems
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2014
SP  - 125
EP  - 140
VL  - 8
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2014_8_a9/
LA  - ru
ID  - IIGUM_2014_8_a9
ER  - 
%0 Journal Article
%A V. A. Srochko
%A V. G. Antonik
%A E. V. Aksenyushkina
%T Sufficient Optimality Conditions Based on Functional Increment Formulas in Control Problems
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2014
%P 125-140
%V 8
%U http://geodesic.mathdoc.fr/item/IIGUM_2014_8_a9/
%G ru
%F IIGUM_2014_8_a9
V. A. Srochko; V. G. Antonik; E. V. Aksenyushkina. Sufficient Optimality Conditions Based on Functional Increment Formulas in Control Problems. The Bulletin of Irkutsk State University. Series Mathematics, Tome 8 (2014), pp. 125-140. http://geodesic.mathdoc.fr/item/IIGUM_2014_8_a9/

[1] Antipina N. V., Dychta V. A., “Linear funtions of Lyapunov–Krotov and sufficient optimality conditions in the form of maximum principle”, Izvestia vuzov. Matematika, 2002, no. 12, 11–22 (in Russian)

[2] Gabasov R., Kirillova F. M., The maximum principle in optimal control theory, Librokom, M., 2011, 272 pp. (in Russian) | MR

[3] Clark F., Optimization an non-smooth analysis, Nauka, M., 1988, 280 pp. (in Russian) | MR

[4] Krotov V. F., Gurman V. I., Methods and problems of optimal control, Nauka, M., 1988, 446 pp. (in Russian) | MR | Zbl

[5] Nikolsky M. S., “On sufficiency of Pontryagin's maximum principle in some optimization problems”, Vestnik Moskovskogo universiteta. Seria 15, 2005, no. 1, 35–43 (in Russian)

[6] Pontryagin L. S., Boltiansky V. G., Gamkrelidze R. V., Mischenko E. F., Mathematical theory of optimal proccesses, Fizmatlit, M., 1961, 388 pp. (in Russian) | MR

[7] Srochko V. A., Iteration methods for solving of optimal control problems, Fizmatlit, M., 2000, 160 pp. (in Russian)

[8] Srochko V. A., Ahmedzhanova N. S., “Analysis and solution of one bilinear optimal control problem”, Vestnik Buriatskogo universiteta. Seria 13, 2005, no. 2, 143–148 (in Russian)

[9] Khailov E. N., “On extremal controls in homogeneous bilinear system”, Trudy MIAN, 220, 1998, 217–235 (in Russian) | Zbl

[10] O. L. Mangasarian, “Sufficient conditions for the optimal control of nonlinear systems”, SIAM J. Control Optim., 4 (1966), 139–152 | DOI | MR | Zbl

[11] A. Swierniak, “Cell cycle as an object of control”, Journal of Biological Systems, 3:1 (1995), 41–54 | DOI