State parametrization method based on shifted Legendre polynomials for solving fractional optimal control problems

DOI10.1007/s40819-017-0475-5zbMath1381.49016OpenAlexW2776494786MaRDI QIDQ1688797

Reza Dehghan

Publication date: 11 January 2018

Published in: International Journal of Applied and Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40819-017-0475-5

zbMATH Keywords

numerical methodparametric optimizationnonlinear optimizationshifted Legendre polynomialsfractional optimal control

Mathematics Subject Classification ID

Nonconvex programming, global optimization (90C26) Sensitivity, stability, parametric optimization (90C31) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Optimality conditions for problems involving ordinary differential equations (49K15)

Cites Work

• A numerical technique based on the shifted Legendre polynomials for solving the time-fractional coupled KdV equations
• A Jacobi Gauss-Lobatto and Gauss-Radau collocation algorithm for solving fractional Fokker-Planck equations
• Free final time fractional optimal control problems
• Fractional sub-equation method and its applications to nonlinear fractional PDEs
• Legendre wavelets method for solving fractional partial differential equations with Dirichlet boundary conditions
• Time-optimal control of systems with fractional dynamics
• A tau approach for solution of the space fractional diffusion equation
• Implicit compact difference schemes for the fractional cable equation
• Numerical solutions of the space- and time-fractional coupled Burgers equations by generalized differential transform method
• Recent history of fractional calculus
• Second kind shifted Chebyshev polynomials for solving space fractional order diffusion equation
• A discrete method to solve fractional optimal control problems
• Fractional control of heat diffusion systems
• An approximate method for numerically solving fractional order optimal control problems of general form
• A new operational matrix for solving fractional-order differential equations
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• On generalized fractional kinetic equations involving generalized Bessel function of the first kind
• A pseudospectral method for fractional optimal control problems
• Numerical solution of the two-sided space-time fractional telegraph equation via Chebyshev tau approximation
• Quasi-compact finite difference schemes for space fractional diffusion equations
• Fractional difference/finite element approximations for the time-space fractional telegraph equation
• New quadrature approach based on operational matrix for solving a class of fractional variational problems
• A numerical method for solving optimal control problems using state parametrization
• A general formulation and solution scheme for fractional optimal control problems
• Kernel-based approximation for Cauchy problem of the time-fractional diffusion equation
• Solving Fixed Final Time Fractional Optimal Control Problems Using the Parametric Optimization Method
• The use of a Legendre multiwavelet collocation method for solving the fractional optimal control problems
• A Central Difference Numerical Scheme for Fractional Optimal Control Problems
• Homotopy Method for Parameter Determination of SoluteTransport with Fractional Advection-dispersion Equation
• Solving multi-dimensional fractional optimal control problems with inequality constraint by Bernstein polynomials operational matrices
• A Formulation and Numerical Scheme for Fractional Optimal Control Problems
• A Fractional Adaptation Scheme for Lateral Control of an AGV
• A Hamiltonian Formulation and a Direct Numerical Scheme for Fractional Optimal Control Problems
• A numerical solution for fractional optimal control problems via Bernoulli polynomials
• A new method based on legendre polynomials for solution of system of fractional order partial differential equations
• Solving fractional optimal control problems within a Chebyshev–Legendre operational technique
• CHAOS SYNCHRONIZATION OF FRACTIONAL-ORDER DIFFERENTIAL SYSTEMS
• ON OPTIMAL SELECTION OF INTERIOR POINTS FOR APPLYING DISCRETIZED BOUNDARY CONDITIONS IN DQ VIBRATION ANALYSIS OF BEAMS AND PLATES
• Quantum Variational Calculus
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: State parametrization method based on shifted Legendre polynomials for solving fractional optimal control problems