Sensitivity Analysis of Value Functional of Fractional Optimal Control Problem with Application to Feedback Construction of Near Optimal Controls

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Sensitivity Analysis of Value Functional of Fractional Optimal Control Problem with Application to Feedback Construction of Near Optimal Controls. / Gomoyunov, Mikhail.
In: Applied Mathematics and Optimization, Vol. 88, No. 2, 41, 01.10.2023.

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

BibTeX

@article{c7087941e41341de91f3b7ef6db87126,

title = "Sensitivity Analysis of Value Functional of Fractional Optimal Control Problem with Application to Feedback Construction of Near Optimal Controls",

abstract = "We consider an optimal control problem for a dynamical system described by a Caputo fractional differential equation of order α∈(0,1) and a terminal cost functional. We prove that, under certain assumptions, the (non-smooth, in general) value functional of this problem has a property of directional differentiability of order α. As an application of this result, we propose a new method for constructing an optimal positional (feedback) control strategy, which allows us to generate ε-optimal controls for any predetermined accuracy ε>0.",

author = "Mikhail Gomoyunov",

note = "This work was supported by RSF, project no. 19–11–00105.",

year = "2023",

month = oct,

day = "1",

doi = "10.1007/s00245-023-10022-4",

language = "English",

volume = "88",

journal = "Applied Mathematics and Optimization",

issn = "0095-4616",

publisher = "Springer New York",

number = "2",

}

RIS

TY - JOUR

T1 - Sensitivity Analysis of Value Functional of Fractional Optimal Control Problem with Application to Feedback Construction of Near Optimal Controls

AU - Gomoyunov, Mikhail

N1 - This work was supported by RSF, project no. 19–11–00105.

PY - 2023/10/1

Y1 - 2023/10/1

N2 - We consider an optimal control problem for a dynamical system described by a Caputo fractional differential equation of order α∈(0,1) and a terminal cost functional. We prove that, under certain assumptions, the (non-smooth, in general) value functional of this problem has a property of directional differentiability of order α. As an application of this result, we propose a new method for constructing an optimal positional (feedback) control strategy, which allows us to generate ε-optimal controls for any predetermined accuracy ε>0.

AB - We consider an optimal control problem for a dynamical system described by a Caputo fractional differential equation of order α∈(0,1) and a terminal cost functional. We prove that, under certain assumptions, the (non-smooth, in general) value functional of this problem has a property of directional differentiability of order α. As an application of this result, we propose a new method for constructing an optimal positional (feedback) control strategy, which allows us to generate ε-optimal controls for any predetermined accuracy ε>0.

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85161034138

UR - https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=tsmetrics&SrcApp=tsm_test&DestApp=WOS_CPL&DestLinkType=FullRecord&KeyUT=001003459400001

U2 - 10.1007/s00245-023-10022-4

DO - 10.1007/s00245-023-10022-4

M3 - Article

VL - 88

JO - Applied Mathematics and Optimization

JF - Applied Mathematics and Optimization

SN - 0095-4616

IS - 2

M1 - 41

ER -

ID: 40099381