Solving the Optimal Control of Volterra-Fredholm integro-differential equation via Müntz polynomials

Abstract

The main goal of the current paper is to present a direct numericalmethod for solving optimal control problem for systems governed by Volterra-Fredholm integro-differential equation. This method is based upon a new form of orthogonal M¨untz-Legendre polynomials, and collocation method to transform the optimal control problem to a nonlinear programming problem with finite-dimensional.
The accuracy and efficiency of the proposed method are examined with illustrative examples.

Key words and phrases. Optimal control problem, Volterra-Fredholm integro-differential equation, M¨untz-Legendre polynomials, Legendre-Gauss-Lobatto points, Legendre-Gauss-Lobatto quadrature.

2000 Mathematics Subject Classification. 34H05,45A05, 45J05