Optimal control of a class of Caputo fractional systems

被引：1

作者：

Das, Sanjukta ^{[1
]}

Tripathi, Vidushi ^{[1
]}

机构：

[1] Mahindra Univ, Ecole Cent Sch Engn, Hyderabad 500043, India

来源：

JOURNAL OF ANALYSIS | 2025年 / 33卷 / 01期

关键词：

Fractional calculus; Optimal control; Pontryagin maximum principle; Necessary conditions; HJB equation; PONTRYAGIN MAXIMUM PRINCIPLE; EQUATIONS; CONTROLLABILITY;

D O I：

10.1007/s41478-024-00840-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This article introduces a broad formulation of fractional optimal control issues characterized by a class of Caputo fractional systems within Hilbert spaces. Through a variational method, the Pontryagin maximum principle (PMP) is established as a set of essential conditions for optimality. Following this, the Hamilton-Jacobi-Bellman (HJB) equations are derived based on the derived PMP. In conclusion, it is established that the value function serves as a viscosity solution of the HJB equation. Numerical example is finally provided to exemplify the theory developed.

引用

页码：387 / 408

页数：22

共 50 条

[41] Optimal control of ensembles of dynamical systems [J].

Scagliotti, Alessandro .

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2023, 29

[42] The necessary conditions for finite horizon time varying order optimal control of Caputo systems [J].

Tabatabaei, S. Sepehr ;

Yazdanapanah, Mohammad Javad ;

Tavazoei, Mohammad Saleh .

IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION, 2018, 35 (04) :1087-1102

[43] Research on controllability for a class of fractional-orderlinear control systems [J].

Zeng Qingshan Cao Guangyi Zhu XinjianDepartment of Automation Shanghai Jiaotong University Shanghai P R China .

JournalofSystemsEngineeringandElectronics, 2005, (02) :376-381

[44] ON FRACTIONAL HAMILTONIAN SYSTEMS POSSESSING FIRST-CLASS CONSTRAINTS WITHIN CAPUTO DERIVATIVES [J].

Baleanu, Dumitru ;

Muslih, Sami I. ;

Rabei, Eqab M. ;

Golmankhaneh, Alireza K. ;

Golmankhaneh, Ali K. .

ROMANIAN REPORTS IN PHYSICS, 2011, 63 (01) :3-8

[45] Optimal control problems governed by a class of nonlinear systems [J].

Sidi, Maawiya Ould ;

Zine, Rabie ;

Mahmoud, Sid Ahmed Ould Ahmed ;

Alshammari, Hadi Obaid ;

Beinane, Sid Ahmed Ould .

AIMS MATHEMATICS, 2024, 9 (01) :440-452

[46] OPTIMAL CONTROL OF A CLASS OF DISTRIBUTED PARAMETER DELAY SYSTEMS [J].

XIANG Xiao ling Department of Mathematics Guizhou University Guiyang China .

Systems Science and Mathematical Sciences, 2000, (01) :31-41

[47] Optimal Controls for a Class of Conformable Fractional Evolution Systems [J].

Liang, Yue .

FRACTAL AND FRACTIONAL, 2023, 7 (09)

[48] Optimal fractional order control for nonlinear systems represented by the Euler-Lagrange formulation [J].

Azar, Ahmad Taher ;

Serrano, Fernando E. ;

Kamal, Nashwa Ahmad .

INTERNATIONAL JOURNAL OF MODELLING IDENTIFICATION AND CONTROL, 2021, 37 (01) :1-9

[49] A general numerical scheme for the optimal control of fractional Birkhoffian systems [J].

Lin He ;

Chunqiu Wei ;

Jiang Sha ;

Delong Mao ;

Kangshuo Wang .

Nonlinear Dynamics, 2022, 110 :1543-1557

[50] Numerical Solution of the Optimal Control for Fractional Order Singular Systems [J].

Moubarak, M. R. A. ;

Ahmed, H. F. ;

Khorshi, Omar .

DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS, 2018, 26 (1-3) :279-291

← 1 2 3 4 5 →