Journal of Mathematical Finance, Volume (1), No (1), Year (2011-5) , Pages (8-13)

Title : ( Legendre Method for a Class of Nonlinear Optimal control problems )

Authors: ali reza ziae tohidi , Omid Navid Samadi , Mohammad Hadi Farahi ,

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Abstract This paper introduces a numerical technique for solving a class of optimal control problems containing nonlinear dynamical system and functional of state variables. This numerical method consists of two major parts. In the first part, using linear combination property of intervals, we convert the nonlinear dynamical system into an equivalent linear system. And in the second part, which we are dealing with a linear dynamical system, using Legendre expansions for approximating both the state and associated control together with discretizing the constraints over the Chebyshev-Gauss-Lobatto points, the optimal control problem is transformed into a corresponding NLP problem which is diretly solved. The proposed idea is illustrated by several numerical examples.


, Keywords: Optimal Control, Legendre Polynomials, Linear Combination Property of Intervals, Chebyshev-Gauss-Lobatto Points, Nonlinear Programming
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author = {Ziae Tohidi, Ali Reza and Navid Samadi, Omid and Farahi, Mohammad Hadi},
title = {Legendre Method for a Class of Nonlinear Optimal control problems},
journal = {Journal of Mathematical Finance},
year = {2011},
volume = {1},
number = {1},
month = {May},
issn = {4236-2011},
pages = {8--13},
numpages = {5},
keywords = {Keywords: Optimal Control; Legendre Polynomials; Linear Combination Property of Intervals; Chebyshev-Gauss-Lobatto Points; Nonlinear Programming},


%0 Journal Article
%T Legendre Method for a Class of Nonlinear Optimal control problems
%A Ziae Tohidi, Ali Reza
%A Navid Samadi, Omid
%A Farahi, Mohammad Hadi
%J Journal of Mathematical Finance
%@ 4236-2011
%D 2011