A Simple Accurate Method for Solving Fractional Variational and Optimal Control Problems

Abstract

We develop a simple and accurate method to solve fractional variational and fractional optimal control problems with dependence on Caputo and Riemann-Liouville operators. Using known formulas for computing fractional derivatives of polynomials, we rewrite the fractional functional dynamical optimization problem as a classical static optimization problem. The method for classical optimal control problems is called Ritz's method. Examples show that the proposed approach is more accurate than recent methods available in the literature.

arXiv commentThis is a preprint of a paper whose final and definite form will be published in 'Journal of Optimization Theory and Applications', ISSN 0022-3239 (print), ISSN 1573-2878 (electronic). Paper Submitted 31-Dec-2014; Revised 21-Oct-2015 and 17-Jan-2016; Accepted 24-Jan-2016

References in corpus (9)

• Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives
• Fractional conservation laws in optimal control theory
• Fractional Optimal Control in the Sense of Caputo and the Fractional Noether's Theorem
• Fractional Order Optimal Control Problems with Free Terminal Time
• A Discrete Method to Solve Fractional Optimal Control Problems
• Numerical Approximations of Fractional Derivatives with Applications
• Leitmann's direct method for fractional optimization problems
• Numerical solution of fractional Sturm-Liouville equation in integral form
• A Generalized Fractional Calculus of Variations

Cited by in corpus (5)

• Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems
• Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection
• Fractional Herglotz Variational Principles with Generalized Caputo Derivatives
• Enlarged Controllability of Riemann-Liouville Fractional Differential Equations
• Fractional Order Version of the HJB Equation