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
scimago Q1
wos Q1
SJR: 1.316
CiteScore: 4.4
Impact factor: 2.4
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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Total citations:
36
Citations from 2024:
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(16.67%)
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GOST
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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
RIS
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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 -
Cite this
BibTex (up to 50 authors)
Copy
@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}
}
Cite this
MLA
Copy
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.