An efficient computational method based on the hat functions for solving fractional optimal control problems

DOI10.1515/TMJ-2016-0007zbMath1341.49038OpenAlexW2313267268MaRDI QIDQ278219

Carlo Cattani, Ali Shakiba, Mohammad Reza Hooshmandasl, Mohammad Heydari

Publication date: 2 May 2016

Published in: Tbilisi Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/tmj-2016-0007

zbMATH Keywords

Lagrange multiplierscomputational methodoperational matrixfractional optimal control problemshat functions

Mathematics Subject Classification ID

Numerical methods based on necessary conditions (49M05) Fractional derivatives and integrals (26A33) Existence theories for optimal control problems involving ordinary differential equations (49J15) Optimality conditions for problems involving ordinary differential equations (49K15) Fractional ordinary differential equations (34A08)

Related Items (7)

Chebyshev cardinal functions for a new class of nonlinear optimal control problems generated by Atangana-Baleanu-Caputo variable-order fractional derivative ⋮ Piecewise Chebyshev cardinal functions: application for constrained fractional optimal control problems ⋮ An efficient computational approach for linear and nonlinear fractional differential equations ⋮ An efficient analytical technique for fractional model of vibration equation ⋮ Numerical solution of nonlinear 2D optimal control problems generated by Atangana-Riemann-Liouville fractal-fractional derivative ⋮ A direct method based on the Chebyshev polynomials for a new class of nonlinear variable-order fractional 2D optimal control problems ⋮ A new class of orthonormal basis functions: application for fractional optimal control problems

Cites Work

• On the existence of optimal solutions to fractional optimal control problems
• A review of operational matrices and spectral techniques for fractional calculus
• A computational method for solving stochastic Itô-Volterra integral equations based on stochastic operational matrix for generalized hat basis functions
• Optimality conditions and a solution scheme for fractional optimal control problems
• A new numerical algorithm to solve fractional differential equations based on operational matrix of generalized hat functions
• A numerical technique for solving a class of fractional variational problems
• Epsilon-Ritz method for solving a class of fractional constrained optimization problems
• A numerical method for solving systems of linear and nonlinear integral equations of the second kind by hat basis functions
• A numerical technique for solving fractional optimal control problems
• Optimal control of a fractional diffusion equation with state constraints
• Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives
• An efficient computational method for solving nonlinear stochastic Itô integral equations: application for stochastic problems in physics
• Calculus of variations with fractional derivatives and fractional integrals
• Numerical approach to differential equations of fractional order
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• The necessary conditions of fractional optimal control in the sense of Caputo
• Model reference adaptive control in fractional order systems using discrete-time approximation methods
• Optimal synergetic control for fractional-order systems
• A general finite element formulation for fractional variational problems
• Fractional variational optimal control problems with delayed arguments
• Numerical solution of a class of fractional optimal control problems via the Legendre orthonormal basis combined with the operational matrix and the Gauss quadrature rule
• An Efficient Numerical Scheme for Solving Multi-Dimensional Fractional Optimal Control Problems With a Quadratic Performance Index
• A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems
• Solving fractional optimal control problems within a Chebyshev–Legendre operational technique

This page was built for publication: An efficient computational method based on the hat functions for solving fractional optimal control problems