Comments on ‘Sweep algorithm for solving optimal control problem with multi-point boundary conditions’ by M Mutallimov, R Zulfuqarova, and L Amirova
- Fikret A Aliev^{1}Email author
Received: 8 October 2015
Accepted: 21 March 2016
Published: 13 May 2016
Abstract
A counter example is given for the solution of the linear-quadratic optimization problem with three-point boundary conditions. The example shows that the solution obtained in (Mutallimov et al. in Adv. Differ. Equ. 2015:233, 2015) by using a sweep method is not optimal.
Keywords
1 Introduction
In [1] the linear-quadratic optimization problem with multi-point boundary conditions, both in the continuous and the discrete cases, are considered. The sweep method [2, 3], which generalizes the results [4] for the two-point boundary conditions is given in [5]. However, the results obtained for the discrete case [1] are not optimal.
Declarations
Acknowledgements
The author thanks the reviewers of the comments and the editors for their instructive remarks.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
- Mutallimov, MM, Zulfugarova, RH, Amirova, LI: Sweep algorithm for solving optimal control problem with multi-point boundary conditions. Adv. Differ. Equ. 2015, 233 (2015) MathSciNetView ArticleGoogle Scholar
- Abramov, AA: On the transfer of boundary conditions for systems of ordinary linear differential equations (a variant of dispersive method). USSR Comput. Math. Math. Phys. 1(3), 617-622 (1962) View ArticleMATHGoogle Scholar
- Aliev, FA, Larin, VB: On the algorithm for solving discrete periodic Riccati equation. Appl. Comput. Math. 13(1), 46-54 (2014) MathSciNetGoogle Scholar
- Aliev, FA: Methods of Solution for the Application Problems of Optimization of the Dynamic Systems. Elm, Baku (1989) MATHGoogle Scholar
- Tiwari, S, Kumar, M: An initial value technique solve two-point non-linear singularly perturbed boundary value problems. Appl. Comput. Math. 14(2), 150-157 (2015) MathSciNetMATHGoogle Scholar
- Gabasova, OR: On optimal control of linear hybrid systems with terminal constraints. Appl. Comput. Math. 13(2), 194-205 (2014) MathSciNetMATHGoogle Scholar
- Rashidinia, J, Khazaei, M, Nikmarvani, H: Spline collocation method for solution of higher order linear boundary value problems. TWMS J. Pure Appl. Math. 6(1), 38-47 (2015) MathSciNetMATHGoogle Scholar