SIAM Journal on Control and Optimization, volume 56, issue 1, pages 102-119
High Order Discrete Approximations to Mayer's Problems for Linear Systems
1
Laboratoire de Mathématiques Informatique et Applications
2
Dipartimento di Matematica [Roma II]
3
ORCOS
Publication type: Journal Article
Publication date: 2018-01-05
Q1
Q1
SJR: 1.565
CiteScore: 4.0
Impact factor: 2.2
ISSN: 03630129, 10957138
Applied Mathematics
Control and Optimization
Abstract
This paper presents a discretization scheme for Mayer's type optimal control problems of linear systems. The scheme is based on second order Volterra--Fliess approximations, and on an augmentation of the control variable in a control set of higher dimension. Compared with the existing results, it has the advantage of providing a higher order accuracy, which may make it more efficient when aiming for a certain precision. Error estimations (depending on the controllability index of the system at the solution) are proved by using a recent result about stability of the optimal solution with respect to disturbances. Numerical results are provided which show the sharpness of the error estimations.
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Pietrus A., Scarinci T., Veliov V. High Order Discrete Approximations to Mayer's Problems for Linear Systems // SIAM Journal on Control and Optimization. 2018. Vol. 56. No. 1. pp. 102-119.
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Pietrus A., Scarinci T., Veliov V. High Order Discrete Approximations to Mayer's Problems for Linear Systems // SIAM Journal on Control and Optimization. 2018. Vol. 56. No. 1. pp. 102-119.
Cite this
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TY - JOUR
DO - 10.1137/16M1079142
UR - https://doi.org/10.1137/16M1079142
TI - High Order Discrete Approximations to Mayer's Problems for Linear Systems
T2 - SIAM Journal on Control and Optimization
AU - Pietrus, Alain
AU - Scarinci, Teresa
AU - Veliov, Vladimir
PY - 2018
DA - 2018/01/05
PB - Society for Industrial and Applied Mathematics (SIAM)
SP - 102-119
IS - 1
VL - 56
SN - 0363-0129
SN - 1095-7138
ER -
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BibTex (up to 50 authors)
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@article{2018_Pietrus,
author = {Alain Pietrus and Teresa Scarinci and Vladimir Veliov},
title = {High Order Discrete Approximations to Mayer's Problems for Linear Systems},
journal = {SIAM Journal on Control and Optimization},
year = {2018},
volume = {56},
publisher = {Society for Industrial and Applied Mathematics (SIAM)},
month = {jan},
url = {https://doi.org/10.1137/16M1079142},
number = {1},
pages = {102--119},
doi = {10.1137/16M1079142}
}
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Pietrus, Alain, et al. “High Order Discrete Approximations to Mayer's Problems for Linear Systems.” SIAM Journal on Control and Optimization, vol. 56, no. 1, Jan. 2018, pp. 102-119. https://doi.org/10.1137/16M1079142.