Transformation preserving controllability for nonlinear optimal
control problems with joint boundary conditions

J 2021

Transformation preserving controllability for nonlinear optimal control problems with joint boundary conditions

ŠIMON HILSCHER, Roman a Vera Michel ZEIDAN

Základní údaje

Originální název

Transformation preserving controllability for nonlinear optimal control problems with joint boundary conditions

Autoři

ŠIMON HILSCHER, Roman (203 Česká republika, garant, domácí) a Vera Michel ZEIDAN (840 Spojené státy)

Vydání

ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2021, 1292-8119

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Francie

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.708

Kód RIV

RIV/00216224:14310/21:00119059

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1051/cocv/2021068

UT WoS

000675417500004

Klíčová slova anglicky

Optimal control problem; joint (coupled) endpoints; separated endpoints; controllability; strong Pontryagin principle; coercivity; sensitivity analysis; free time problem

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 16. 8. 2021 08:46, Mgr. Marie Šípková, DiS.

Anotace

V originále

In this paper we develop a new approach for optimal control problems with general jointly varying state endpoints (also called coupled endpoints). We present a new transformation of a nonlinear optimal control problem with jointly varying state endpoints and pointwise equality control constraints into an equivalent optimal control problem of the same type but with separately varying state endpoints in double dimension. Our new transformation preserves among other properties the controllability (normality) of the considered optimal control problems. At the same time it is well suited even for the calculus of variations problems with joint state endpoints, as well as for optimal control problems with free initial and/or final time. This work is motivated by the results on the second order Sturm–Liouville eigenvalue problems with joint endpoints by Dwyer and Zettl (1994) and by the sensitivity result for nonlinear optimal control problems with separated state endpoints by the authors (2018).

Návaznosti

GA19-01246S, projekt VaV

Název: Nová oscilační teorie pro lineární hamiltonovské a symplektické systémy

Investor: Grantová agentura ČR, Nová oscilační teorie pro lineární hamiltonovské a symplektické systémy

Citovat

ŠIMON HILSCHER, Roman a Vera Michel ZEIDAN. Transformation preserving controllability for nonlinear optimal control problems with joint boundary conditions. ESAIM: Control, Optimisation and Calculus of Variations. EDP Sciences, 2021, roč. 27, July, s. "75", 35 s. ISSN 1292-8119. Dostupné z: https://dx.doi.org/10.1051/cocv/2021068.

@article{1781917,
   author = {Šimon Hilscher, Roman and Zeidan, Vera Michel},
   article_number = {July},
   doi = {http://dx.doi.org/10.1051/cocv/2021068},
   keywords = {Optimal control problem; joint (coupled) endpoints; separated endpoints; controllability; strong Pontryagin principle; coercivity; sensitivity analysis; free time problem},
   language = {eng},
   issn = {1292-8119},
   journal = {ESAIM: Control, Optimisation and Calculus of Variations},
   title = {Transformation preserving controllability for nonlinear optimal control problems with joint boundary conditions},
   url = {https://doi.org/10.1051/cocv/2021068},
   volume = {27},
   year = {2021}
}

TY  - JOUR
ID  - 1781917
AU  - Šimon Hilscher, Roman - Zeidan, Vera Michel
PY  - 2021
TI  - Transformation preserving controllability for nonlinear optimal control problems with joint boundary conditions
JF  - ESAIM: Control, Optimisation and Calculus of Variations
VL  - 27
IS  - July
SP  - "75"
EP  - "75"
PB  - EDP Sciences
SN  - 12928119
KW  - Optimal control problem
KW  - joint (coupled) endpoints
KW  - separated endpoints
KW  - controllability
KW  - strong Pontryagin principle
KW  - coercivity
KW  - sensitivity analysis
KW  - free time problem
UR  - https://doi.org/10.1051/cocv/2021068
N2  - In this paper we develop a new approach for optimal control problems with general jointly varying state endpoints (also called coupled endpoints). We present a new transformation of a nonlinear optimal control problem with jointly varying state endpoints and pointwise equality control constraints into an equivalent optimal control problem of the same type but with separately varying state endpoints in double dimension. Our new transformation preserves among other properties the controllability (normality) of the considered optimal control problems. At the same time it is well suited even for the calculus of variations problems with joint state endpoints, as well as for optimal control problems with free initial and/or final time. This work is motivated by the results on the second order Sturm–Liouville eigenvalue problems with joint endpoints by Dwyer and Zettl (1994) and by the sensitivity result for nonlinear optimal control problems with separated state endpoints by the authors (2018).
ER  -

ŠIMON HILSCHER, Roman a Vera Michel ZEIDAN. Transformation preserving controllability for nonlinear optimal control problems with joint boundary conditions. \textit{ESAIM: Control, Optimisation and Calculus of Variations}. EDP Sciences, 2021, roč.~27, July, s.~''75'', 35 s. ISSN~1292-8119. Dostupné z: https://dx.doi.org/10.1051/cocv/2021068.

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