A New Formulation of the Fractional Optimal Control Problems Involving Mittag–Leffler Nonsingular Kernel

The aim of this paper is to propose a new formulation of the fractional optimal control problems involving Mittag–Leffler nonsingular kernel. By using the Lagrange multiplier within the calculus of variations and by applying the fractional integration by parts, the necessary optimality conditions ar...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 175; no. 3; pp. 718 - 737
Main Authors Baleanu, Dumitru, Jajarmi, Amin, Hajipour, Mojtaba
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2017
Springer Nature B.V
Subjects
Applications of Mathematics
Boundary value problems
Calculus of variations
Calculus of Variations and Optimal Control; Optimization
Computer simulation
Convolution
Economic models
Engineering
Lagrange multiplier
Mathematical analysis
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimal control
Optimization
Theory of Computation
33E12
49K99
Fractional optimal control
26A33
Mittag–Leffler kernel
Euler method
49XX
Fractional calculus
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Summary:The aim of this paper is to propose a new formulation of the fractional optimal control problems involving Mittag–Leffler nonsingular kernel. By using the Lagrange multiplier within the calculus of variations and by applying the fractional integration by parts, the necessary optimality conditions are derived in terms of a nonlinear two-point fractional boundary value problem. Based on the convolution formula and generalized discrete Grönwall’s inequality, the numerical scheme for solving this problem is developed and its convergence is proved. Numerical simulations and comparative results show that the suggested technique is efficient and provides satisfactory results.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-017-1186-0