Optimal Control of Non-linear Volterra Integral Equations with Weakly Singular Kernels Based on Genocchi Polynomials and Collocation Method

Abstract

We consider a problem of finding the best way to control a system, known as an optimal control problem (OCP), governed by non-linear Volterra Integral Equations with Weakly Singular kernels. The equations are based on Genocchi polynomials. Depending on the applicable properties of Genocchi polynomials, the considered OCP is converted to a non-linear programming problem (NLP). This method is speedy and provides a highly accurate solution with great precision using a small number of basis functions. The convergence analysis of the approach is also provided. The accuracy and flawless performance of the proposed technique and verification of the theory are examined with some examples.