A Legendre Galerkin spectral method for optimal control problems

被引：6

作者：

Chen, Yanping ^{[1
]}

Xia, Nianshi ^{[2
]}

Yi, Nianyu ^{[3
]}

机构：

[1] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

[2] Jimei Univ, Chengyi Coll, Fac Math, Xiamen 361021, Peoples R China

[3] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Peoples R China

来源：

JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY | 2011年 / 24卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Legendre-Galerkin; optimal control; spectral method; MIXED FINITE-ELEMENT; SUPERCONVERGENCE; APPROXIMATION;

D O I：

10.1007/s11424-011-8016-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper considers the Legendre Galerkin spectral approximation for the unconstrained optimal control problems. The authors derive a posteriori error estimate for the spectral approximation scheme of optimal control problem. By choosing the appropriate basis functions, the stiff matrix of the discretization equations is sparse. And the authors use the Fast Legendre Transform to improve the efficiency of this method. Two numerical experiments demonstrating our theoretical results are presented.

引用

页码：663 / 671

页数：9

共 50 条

[21] THE PSEUDOSPECTRAL LEGENDRE METHOD FOR DISCRETIZING OPTIMAL-CONTROL PROBLEMS
ELNAGAR, G
KAZEMI, MA
RAZZAGHI, M
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1995, 40 (10) : 1793 - 1796
[22] Chebyshev-Legendre method for discretizing optimal control problems
张稳
马和平
Journal of Shanghai University(English Edition), 2009, 13 (02) : 113 - 118
[23] Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian
Zhang, Jiaqi
Yang, Yin
Zhou, Zhaojie
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2023, 15 (06) : 1631 - 1654
[24] Discrete Legendre spectral Galerkin method for Urysohn integral equations
Das, Payel
Nelakanti, Gnaneshwar
Long, Guangqing
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2018, 95 (03) : 465 - 489
[25] A Convergent Legendre Spectral Collocation Method for the Variable-Order Fractional-Functional Optimal Control Problems
Pirouzeh, Zahra
Skandari, Mohammad Hadi Noori
Pirbazari, Kameleh Nassiri
JOURNAL OF MATHEMATICS, 2024, 2024
[26] A numerical method for solving optimal control problems via Legendre polynomials
Gu, Yajing
Yan, Hongyan
Zhu, Yuanguo
ENGINEERING COMPUTATIONS, 2020, 37 (08) : 2735 - 2759
[27] Using Galerkin Method for Solving Linear Optimal Control Problems
Liverovskiy, D., I
Shevirev, S. P.
IZVESTIYA SARATOVSKOGO UNIVERSITETA NOVAYA SERIYA-MATEMATIKA MEKHANIKA INFORMATIKA, 2014, 14 (03): : 340 - 349
[28] RITZ-GALERKIN METHOD FOR ABSTRACT OPTIMAL CONTROL PROBLEMS
DANIEL, JW
SIAM JOURNAL ON CONTROL, 1973, 11 (01): : 53 - 63
[29] The Chebyshev-Legendre collocation method for a class of optimal control problems
Zhang, Wen
Ma, Heping
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2008, 85 (02) : 225 - 240
[30] Legendre pseudospectral approximations of optimal control problems
Ross, IM
Fahroo, F
NEW TRENDS IN NONLINEAR DYNAMICS AND CONTROL, AND THEIR APPLICATIONS, 2003, 295 : 327 - 342

← 1 2 3 4 5 →