Solving fractional optimal control problems within a Chebyshev–Legendre operational technique

ABSTRACT

In this manuscript, we report a new operational technique for approximating the numerical solution of fractional optimal control (FOC) problems. The operational matrix of the Caputo fractional derivative of the orthonormal Chebyshev polynomial and the Legendre–Gauss quadrature formula are used, and then the Lagrange multiplier scheme is employed for reducing such problems into those consisting of systems of easily solvable algebraic equations. We compare the approximate solutions achieved using our approach with the exact solutions and with those presented in other techniques and we show the accuracy and applicability of the new numerical approach, through two numerical examples.

KEYWORDS:

• Orthonormal polynomials
• operational matrix
• Gauss quadrature
• Lagrange multiplier method
• fractional optimal control problem

MSC:

• 34A08
• 65M70
• 33C45

Disclosure statement

No potential conflict of interest was reported by the authors.