Optimal control of system governed by nonlinear Volterra integral and fractional derivative equations

This work presents a novel formulation for the numerical solution of optimal control problems related to nonlinear Volterra fractional integral equations systems. A spectral approach is implemented based on the new polynomials known as Chelyshkov polynomials. First, the properties of these polynomials are studied to solve the aforementioned problems. The operational matrices and the Galerkin method are used to discretize the continuous optimal control problems. Thereafter, some necessary conditions are defined according to which the optimal solutions of discrete problems converge to the optimal solution of the continuous ones. The applicability of the proposed approach has been illustrated through several examples. In addition, a comparison is made with other methods for showing the accuracy of the proposed one, resulting also in an improved efficiency.