Optimal Control of Volterra Integrao-Differential Equations: Dickson
Interpolation Polynomials and Collocation Method
Abstract
This paper introduces a new direct scheme based on Dickson polynomials
and collocation points to solve a class of optimal control problems
(OCPs) ruled by Volterra integro-differential equations namely Volterra
integro-OCPs (VI-OCPs). Studies in this regard require to calculate the
corresponding operational matrices for expanding the solution of this
problem in terms of Dickson polynomials. This recommended method allows
us to transform the VI-OCP to a system of algebraic equations for
choosing the coefficients and control parameters optimally. The error
estimation of this technique is also investigated. Finally, some example
are given to bring about the validity and applicability of this approach
in comparison with those obtained from other methods.