An Indirect Spectral Collocation Method Based on Shifted Jacobi Functions for Solving Some Class of Fractional Optimal Control Problems

Abstract

Abstract A new approximation formula of the Riemann-Liouville fractional derivatives is derived based on shifted classical Jacobi polynomial in spectral approximations. This formula is presented to approximate indirect solution of fractional optimal control problems (FOCPs) with a fractional differential equation as the dynamic constrain. The properties of new formula allows us to use spectral collocation method to reduce FOCPs by indirect method to a system of liner/nonlinear algebraic equations. Four test examples are presented to examine the applicability and validity of a newly purposed method.