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An efficient hybrid pseudo-spectral method for solving optimal control of Volterra integral systems

Khosrow Maleknejad
Organization: School of Mathematics, Iran University of Science and Technology,
Asyieh Ebrahimzadeh
Organization: School of Mathematics, Iran University of Science and Technology,
Journal / Anthology

Year: 2014
Volume: 19
Page range: 417435

In this paper, a new pseudo-spectral (PS) method is developed for solving op- timal control problems governed by the non-linear Volterra integral equation (VIE). The novel method is based upon approximating the state and control variables by the hybrid of block pulse functions and Legendre polynomials. The properties of hybrid functions are presented. The numerical integration and collocation method is utilized to discretize the continuous optimal control problem and then the resulting large-scale finite-dimensional non-linear programming (NLP) is solved by the existing well-developed algorithm in Math- ematica software. A set of sufficient conditions is presented under which optimal solutions of discrete optimal control problems converge to the optimal solution of the continuous problem. The error bound of approximation is also given. Numerical experiments con- firm efficiency of the proposed method especially for problems with non-sufficiently smooth solutions belonging to class C1 or C2.