Ultraspherical integral method for optimal control problems governed by ordinary differential equations

被引：28

作者：

El-Hawary, HM ^{[1
]}

Salim, MS

Hussien, HS

机构：

[1] Assiut Univ, Fac Sci, Dept Math, Assiut, Egypt

[2] El Azhar Univ, Fac Sci, Dept Math, Assiut, Egypt

[3] S Valley Univ, Fac Sci, Dept Math, Qena, Egypt

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2003年 / 25卷 / 03期

关键词：

spectral methods; approximation by ultraspherical polynomials; penalty leap frog method; differential equations; optimal control;

D O I：

10.1023/A:1022463810376

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper an ultraspherical integral method is proposed to solve optimal control problems governed by ordinary differential equations. Ultraspherical approximation method reduced the problem to a constrained optimization problem. Penalty leap frog method is presented to solve the resulting constrained optimization problem. Error estimates for the ultraspherical approximations are derived and a technique that gives an optimal approximation of the problems is introduced. Numerical results are included to confirm the efficiency and accuracy of the method.

引用

页码：283 / 303

页数：21

共 23 条

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Canuto C., 2012, Spectral Methods: Fundamentals in Single Domains

[2] The ultraspherical coefficients of the moments of a general-order derivative of an infinitely differentiable function [J].