In this paper, the Picard’s iteration method is proposed to obtain an approximate analytical solution for linear and nonlinear optimal control problems with quadratic objective functional. It consists in deriving the necessary optimality conditions using the minimum principle of Pontryagin, which result in a two-point-boundary-value-problem (TPBVP). By applying the Picard’s iteration method to the resulting TPBVP, the optimal control law and the optimal trajectory are obtained in the form of a truncated series. The efficiency of the proposed technique for handling optimal control problems is illustrated by four numerical examples, and comparison with other methods is made.
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DOI : 10.1051/ro/2019057
Mots-clés : Optimal control, Pontryagin’s minimum principle, Hamilton–Pontryagin equations, Picard’s iteration method, ordinary differential equations
@article{RO_2020__54_5_1419_0,
author = {Akkouche, Abderrahmane and Aidene, Mohamed},
title = {Solving optimal control problems using the {Picard{\textquoteright}s} iteration method},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {1419--1435},
publisher = {EDP-Sciences},
volume = {54},
number = {5},
year = {2020},
doi = {10.1051/ro/2019057},
mrnumber = {4126313},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2019057/}
}
TY - JOUR AU - Akkouche, Abderrahmane AU - Aidene, Mohamed TI - Solving optimal control problems using the Picard’s iteration method JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2020 SP - 1419 EP - 1435 VL - 54 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2019057/ DO - 10.1051/ro/2019057 LA - en ID - RO_2020__54_5_1419_0 ER -
%0 Journal Article %A Akkouche, Abderrahmane %A Aidene, Mohamed %T Solving optimal control problems using the Picard’s iteration method %J RAIRO - Operations Research - Recherche Opérationnelle %D 2020 %P 1419-1435 %V 54 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2019057/ %R 10.1051/ro/2019057 %G en %F RO_2020__54_5_1419_0
Akkouche, Abderrahmane; Aidene, Mohamed. Solving optimal control problems using the Picard’s iteration method. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 5, pp. 1419-1435. doi : 10.1051/ro/2019057. http://www.numdam.org/articles/10.1051/ro/2019057/
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