Fractional optimal control problem for ordinary differential equation in weighted Lebesgue spaces

被引：11

作者：

Bandaliyev, R. A. ^{[1
,3
]}

Mamedov, I. G. ^{[2
]}

Mardanov, M. J. ^{[1
,4
]}

Melikov, T. K. ^{[1
,2
]}

机构：

[1] NAS Azerbaijan, Inst Math & Mech, Baku, Azerbaijan

[2] NAS Azerbaijan, Inst Control Syst, Baku, Azerbaijan

[3] RUDN Univ, SM Nikolsldi Inst Math, Moscow 117198, Russia

[4] Baku State Univ, Baku, Azerbaijan

来源：

OPTIMIZATION LETTERS | 2020年 / 14卷 / 06期

关键词：

Fractional optimal control problem; Initial value problem; Caputo fractional derivative; Weighed Lebesgue spaces; Pontryagin's maximum principle;

D O I：

10.1007/s11590-019-01518-6

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, a necessary and sufficient condition, such as the Pontryagin's maxi-mum principle for a fractional optimal control problem with concentrated parameters, is given by the ordinary fractional differential equation with a coefficient in weighted Lebesgue spaces. We discuss a formulation of fractional optimal control problems by a fractional differential equation in the sense of Caputo fractional derivative. The statement of the fractional optimal control problem is studied by using a new version of the increment method that essentially uses the concept of an adjoint equation of the integral form.

引用

页码：1519 / 1532

页数：14

共 29 条

[1] Fractional Optimal Control Problems with Several State and Control Variables [J].

Agrawal, Om P. ;

Defterli, Ozlem ;

Baleanu, Dumitru .

JOURNAL OF VIBRATION AND CONTROL, 2010, 16 (13) :1967-1976

[2] A general formulation and solution scheme for fractional optimal control problems [J].

Agrawal, OP .

NONLINEAR DYNAMICS, 2004, 38 (1-4) :323-337

[3] A new approach to the Pontryagin maximum principle for nonlinear fractional optimal control problems [J].

Ali, Hegagi M. ;

Pereira, Fernando Lobo ;

Gama, Silvio M. A. .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2016, 39 (13) :3640-3649

[4]

Alsaedi A, 2018, ELECTRON J DIFFER EQ, V2018, P87

[5]

BACHAR I, 2017, ELECTRON J DIFF 1004

[6]

Baleanu D, 2012, FRACTIONAL DYNAMICS

[7] The optimal control problem in the processes described by the Goursat problem for a hyperbolic equation in variable exponent Sobolev spaces with dominating mixed derivatives [J].

Bandaliyev, R. A. ;

Guliyev, V. S. ;

Mamedov, I. G. ;

Sadigov, A. B. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2016, 305 :11-17

[8] Optimal Control Problem for Bianchi Equation in Variable Exponent Sobolev Spaces [J].

Bandaliyev, Rovshan A. ;

Guliyev, Vagif S. ;

Mamedov, Ilgar G. ;

Rustamov, Yasin I. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2019, 180 (01) :303-320

[9]

Castillo RE, 2016, INTRO COURSE LEBESGU

[10]

Heinonen J., 2001, Lectures on analysis on metric spaces

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