An efficient optimization algorithm for nonlinear 2D fractional optimal control problems

An efficient optimization algorithm for nonlinear 2D fractional optimal control problems

In this research article, we present an optimization algorithm aimed at finding the optimal solution for nonlinear 2-dimensional fractional optimal control problems that arise from nonlinear fractional dynamical systems governed by Caputo derivatives under Goursat–Darboux conditions. The system dyna...

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Bibliographic Details
Published in:The Journal of supercomputing Vol. 80; no. 6; pp. 7906 - 7930
Main Authors: Moradikashkooli, A., Haj Seyyed Javadi, H., Jabbehdari, S.
Format: Journal Article
Language:English
Published: New York Springer US 01-04-2024
Springer Nature B.V
Subjects:
Algorithms
Basis functions
Compilers
Computer Science
Dynamical systems
Interpreters
Lagrange multiplier
Mathematical analysis
Optimal control
Optimization
Optimization algorithms
Polynomials
Processor Architectures
Programming Languages
Quadratures
System dynamics
Wave equations
Operational matrix
Nonlinear 2D fractional optimal control problems
Optimization algorithm
Coefficients and parameters
Generalized Laguerre polynomials
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Summary:In this research article, we present an optimization algorithm aimed at finding the optimal solution for nonlinear 2-dimensional fractional optimal control problems that arise from nonlinear fractional dynamical systems governed by Caputo derivatives under Goursat–Darboux conditions. The system dynamics are described by equations such as the Klein–Gordon, convection–diffusion, and diffusion–wave equations. Our algorithm utilizes a novel class of basis functions called generalized Laguerre polynomials (GLPs), which are an extension of the traditional Laguerre polynomials. To begin, we introduce the GLPs and their properties, and we develop several new operational matrices specifically tailored for these basis functions. Next, we expand the state and control functions using the GLPs, with the coefficients and control parameters remaining unknown. This expansion allows us to transform the original problem into an algebraic system of equations. To facilitate this transformation, we employ operational matrices of Caputo derivatives, the rule of 2D Gauss–Legendre quadrature, and the method of Lagrange multipliers.
ISSN:0920-8542
1573-0484
DOI:10.1007/s11227-023-05732-z