A New Direct Method for Solving Optimal Control Problem of Nonlinear Volterra–Fredholm Integral Equation via the Müntz–Legendre Polynomials

Abstract

In this study, a new pseudo-spectral method is proposed to numerical solve of an optimal control problem whose constraint is given in terms of integral equation. The computational technique is based on a special form of the orthogonal Muntz–Legendre polynomials. Using the Legendre–Gauss–Lobatto points and Legendre–Gauss–Lobatto quadrature, the control and state functions are approximated by a finite combination of basis functions. Employing the method of this paper, the main optimal control problem becomes to an equivalent nonlinear programming problem. We also analyze the convergence of the proposed method by applying appropriate conditions. Finally, some examples are included to demonstrate the performance and accuracy of the introduced scheme.