On the Relationship Between the Pontryagin Maximum Principle and the Hamilton–Jacobi–Bellman Equation in Optimal Control Problems for Fractional-Order Systems

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On the Relationship Between the Pontryagin Maximum Principle and the Hamilton–Jacobi–Bellman Equation in Optimal Control Problems for Fractional-Order Systems. / Gomoyunov, M.
In: Differential Equations, Vol. 59, No. 11, 01.11.2023, p. 1520-1526.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{5b7cf2de4d554b71a84048a141e58286,

title = "On the Relationship Between the Pontryagin Maximum Principle and the Hamilton–Jacobi–Bellman Equation in Optimal Control Problems for Fractional-Order Systems",

abstract = "We consider the optimal control problem of minimizing the terminal cost functional for a dynamical system whose motion is described by a differential equation with Caputo fractional derivative. The relationship between the necessary optimality condition in the form of Pontryagin{\textquoteright}s maximum principle and the Hamilton–Jacobi–Bellman equation with so-called fractional coinvariant derivatives is studied. It is proved that the costate variable in the Pontryagin maximum principle coincides, up to sign, with the fractional coinvariant gradient of the optimal result functional calculated along the optimal motion.",

author = "M. Gomoyunov",

note = "This work was financially supported by the Russian Science Foundation, project 19-11-00105, https://rscf.ru/en/project/19-11-00105/.",

year = "2023",

month = nov,

day = "1",

doi = "10.1134/S0012266123011006X",

language = "English",

volume = "59",

pages = "1520--1526",

journal = "Differential Equations",

issn = "0012-2661",

publisher = "Pleiades Publishing",

number = "11",

}

RIS

TY - JOUR

T1 - On the Relationship Between the Pontryagin Maximum Principle and the Hamilton–Jacobi–Bellman Equation in Optimal Control Problems for Fractional-Order Systems

AU - Gomoyunov, M.

N1 - This work was financially supported by the Russian Science Foundation, project 19-11-00105, https://rscf.ru/en/project/19-11-00105/.

PY - 2023/11/1

Y1 - 2023/11/1

N2 - We consider the optimal control problem of minimizing the terminal cost functional for a dynamical system whose motion is described by a differential equation with Caputo fractional derivative. The relationship between the necessary optimality condition in the form of Pontryagin’s maximum principle and the Hamilton–Jacobi–Bellman equation with so-called fractional coinvariant derivatives is studied. It is proved that the costate variable in the Pontryagin maximum principle coincides, up to sign, with the fractional coinvariant gradient of the optimal result functional calculated along the optimal motion.

AB - We consider the optimal control problem of minimizing the terminal cost functional for a dynamical system whose motion is described by a differential equation with Caputo fractional derivative. The relationship between the necessary optimality condition in the form of Pontryagin’s maximum principle and the Hamilton–Jacobi–Bellman equation with so-called fractional coinvariant derivatives is studied. It is proved that the costate variable in the Pontryagin maximum principle coincides, up to sign, with the fractional coinvariant gradient of the optimal result functional calculated along the optimal motion.

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85181205211

UR - https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=tsmetrics&SrcApp=tsm_test&DestApp=WOS_CPL&DestLinkType=FullRecord&KeyUT=001131565100001

U2 - 10.1134/S0012266123011006X

DO - 10.1134/S0012266123011006X

M3 - Article

VL - 59

SP - 1520

EP - 1526

JO - Differential Equations

JF - Differential Equations

SN - 0012-2661

IS - 11

ER -

ID: 50621417