Optimal control of Volterra integral equations of third kind using Krall–Laguerre Polynomials

Abstract

A novel method has been introduced to dissolve optimal control problems in systems governed by third-kind Volterra integral equations. This method utilizes Krall–Laguerre Polynomials as a basis function for expanding functions. By transforming the optimal control problem governed by third-kind Volterra integral equations (OCVIE3k) into a nonlinear programming problem (NLP), the solution process is significantly simplified. This approach involves converting the original problem into a more manageable form, which can be solved using established optimization techniques. The effectiveness and reliability of this proposed method are evaluated by comparing its outcomes to exact solutions when available.