Spectral homotopy analysis method and its convergence for solving a class of nonlinear optimal control problems

被引：0
作者：
H. Saberi Nik
S. Effati
S. S. Motsa
M. Shirazian
机构：
[1] Ferdowsi University of Mashhad,Department of Applied Mathematics, School of Mathematical Sciences
[2] Ferdowsi University of Mashhad,Center of Excellence on Soft Computing and Intelligent Information Processing (SCIIP)
[3] University of KwaZulu-Natal,School of Mathematical Sciences
[4] University of Neyshabur,Department of Mathematics
来源：
Numerical Algorithms | 2014年 / 65卷
关键词：
Spectral homotopy analysis method; Optimal control problems; Pontryagin’s maximum principle; Spectral collocation;
D O I：
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中图分类号：
学科分类号：
摘要：
A combination of the hybrid spectral collocation technique and the homotopy analysis method is used to construct an iteration algorithm for solving a class of nonlinear optimal control problems (NOCPs). In fact, the nonlinear two-point boundary value problem (TPBVP), derived from the Pontryagin’s Maximum Principle (PMP), is solved by spectral homotopy analysis method (SHAM). For the first time, we present here a convergence proof for SHAM. We treat in detail Legendre collocation and Chebyshev collocation. It is indicated that Legendre collocation gives the same numerical results with Chebyshev collocation. Comparisons are made between SHAM, Matlab bvp4c generated results and results from literature such as homotopy perturbation method (HPM), optimal homotopy perturbation method (OHPM) and differential transformations.
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页码：171 / 194
页数：23
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