201. Optimal control of system governed by nonlinear Volterra integral and fractional derivative equations
- Author
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Leila Moradi, Beatrice Paternoster, Francesco Palmieri, Eslam Farsimadan, and Dajana Conte
- Subjects
Riemann–Liouville integral ,Chelyshkov polynomials ,Volterra fractional integral equations ,Fractional calculus ,Work (thermodynamics) ,Spectral approach ,Discretization ,Applied Mathematics ,010103 numerical & computational mathematics ,Optimal control ,01 natural sciences ,Integral equation ,010101 applied mathematics ,Computational Mathematics ,Nonlinear system ,Applied mathematics ,0101 mathematics ,Galerkin method ,Mathematics - Abstract
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.
- Published
- 2021