Geodesic
A method for relaxing state constraints in nonsmooth optimal control problems
Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2022), pp. 107-114.

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

In this paper, we consider the optimal control problem described by a system of ordinary differential equations in the presence of state constraints. Theoretical results are obtained concerning the approximation of this problem by a sequence of new optimal control problems with a modified right-hand side of the control system and no state constraints. The issues of the approximation of continuous control systems by their discrete versions are also discussed.
Keywords: Optimal control; state constraints; nonsmooth optimisation; approximation. 
@article{BGUMI_2022_2_a9,
     author = {M. P. Dymkov and S. M. Dymkou},
     title = {A method for relaxing state constraints in nonsmooth optimal control problems},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {107--114},
     publisher = {mathdoc},
     volume = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2022_2_a9/}
}
TY  - JOUR
AU  - M. P. Dymkov
AU  - S. M. Dymkou
TI  - A method for relaxing state constraints in nonsmooth optimal control problems
JO  - Journal of the Belarusian State University. Mathematics and Informatics
PY  - 2022
SP  - 107
EP  - 114
VL  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BGUMI_2022_2_a9/
LA  - en
ID  - BGUMI_2022_2_a9
ER  - 
%0 Journal Article
%A M. P. Dymkov
%A S. M. Dymkou
%T A method for relaxing state constraints in nonsmooth optimal control problems
%J Journal of the Belarusian State University. Mathematics and Informatics
%D 2022
%P 107-114
%V 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BGUMI_2022_2_a9/
%G en
%F BGUMI_2022_2_a9
M. P. Dymkov; S. M. Dymkou. A method for relaxing state constraints in nonsmooth optimal control problems. Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2022), pp. 107-114. http://geodesic.mathdoc.fr/item/BGUMI_2022_2_a9/

[1] A. V. Arutyunov, S. M. Aseev, “Investigation of the degeneracy phenomenon of the maximum principle for optimal control problems with state constraints”, SIAM Journal on Control and Optimization, 35:3 (1997), 930–952 | DOI | MR | Zbl

[2] B. S. Mordukhovich, “Discrete approximations and refined Euler – Lagrange conditions for nonconvex differential inclusions”, SIAM Journal on Control and Optimization, 33:3 (1995), 882–915 | DOI | MR | Zbl

[3] R. F. Hartl, S. P. Sethi, R. G. Vickson, “A survey of the maximum principles for optimal control problems with state constraints”, SIAM Review, 37:2 (1995), 181–218 | DOI | MR | Zbl

[4] F. H. Clarke, Optimization and nonsmooth analysis, Willey, New York, 1983, 308 pp. | MR | Zbl

[5] K. L. Teo, C. J. Goh, K. H. Wong, A unified computational approach to optimal control problems, Pitman Monographs and Surveys in Pure and Applied Mathematics, 55, Longman Scientific and Technical, Harlow, 1991, 329 pp. | MR | Zbl

[6] B. Sh. Mordukhovich, Metody approksimatsii v zadachakh optimizatsii i upravleniya, Nauka, Moskva, 1988, 360 pp. | MR

[7] V. V. Gorokhovik, Konechnomernye zadachi optimizatsii, Izdatelskii tsentr BGU, Minsk, 2007, 240 pp. | MR

[8] S. M. Aseev, “Zadacha optimalnogo upravleniya dlya differentsialnogo vklyucheniya s fazovym ogranicheniem. Gladkie approksimatsii i neobkhodimye usloviya optimalnosti”, Trudy mezhdunarodnoi konferentsii, posvyaschennoi 90-letiyu so dnya rozhdeniya LS Pontryagina (Moskva, Rossiya). Geometricheskaya teoriya upravleniya, Itogi Nauki i Tekhniki. Seriya Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 64, VINITI, Moskva, 1999, 57–81 | MR

[9] S. Dymkou, “Approximation of the constrained nonsmooth optimal control problems and their applications for the robot planning motion”, Book of abstracts of 5th International congress on industrial and applied mathematics (Sydney, Australia), ICIAM 2003 Management Committee, Sydney, 2003, 184

[10] V. Demyanov, A. Rubinov, Constructive nonsmooth analysis, Published Verlag Peter Lang, Frankfurt am Main, 1995, 416 pp. | MR

[11] S. Dymkou, M. Dymkov, E. Rogers, K. Galkowski, “Optimal control of non-stationary differential linear repetitive processes”, Integral Equations and Operator Theory, 60:2 (2008), 201–216 | DOI | MR | Zbl

[12] M. Dymkov, E. Rogers, S. Dymkou, K. Galkowski, “Constrained optimal control theory for differential linear repetitive processes”, SIAM Journal on Control and Optimization, 47:1 (2008), 396–420 | DOI | MR | Zbl

[13] M. P. Dymkov, “O strukture resheniya v lineinoi zadache dvizheniya gaza v truboprovode”, Zhurnal Belorusskogo gosudarstvennogo universiteta. Matematika. Informatika, 3 (2017), 27–37