Numerical Solution of Fractional Optimal Control Problems via Lagrange Polynomials

Abstract

A numerical method for solving a class of fractional optimal control problems (FOCPs) is presented. First, the FOCP is transformed into an equivalent variational problem, then using Lagrange polynomials, the problem is reduced to the problem of solving a system of algebraic equations. With the aid of an operational matrix of fractional integration, Gauss quadrature formula and Newton’s iterative method for solving a system of algebraic equations, the problem is solved approximately. Approximate solutions are derived by the method satisfy all the initial conditions of the problem. Finally some illustrative examples are included to demonstrate the applicability of the present technique.

Keywords: Fractional Optimal Control Problems, Lagrange Polynomials, Operational Matrix of Riemann–Liouville Fractional Integration, Numerical Method