Volume 54, Number 5, September-October 2020
|Page(s)||1419 - 1435|
|Published online||23 July 2020|
Solving optimal control problems using the Picard’s iteration method
Département de Mathématiques, Faculté des Sciences et des Sciences Appliquées, Université Akli Mohand Oulhadj de Bouira, 10 000 Bouira, Algeria
2 Laboratoire de Conception et Conduite des Systèmes de Production Université Mouloud Mammeri de Tizi-Ouzou, 15 000 Tizi-Ouzou, Algeria
* Corresponding author: firstname.lastname@example.org
Accepted: 27 May 2019
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.
Mathematics Subject Classification: 49J15 / 93C15
Key words: Optimal control / Pontryagin’s minimum principle / Hamilton–Pontryagin equations / Picard’s iteration method / ordinary differential equations
© EDP Sciences, ROADEF, SMAI 2020
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