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.

Keywords

• Integral equations of third kind
• Optimal control problem
• Krall–Laguerre Polynomials