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

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

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Article ID: iaor2014222
Volume: 65
Issue: 1
Start Page Number: 171
End Page Number: 194
Publication Date: Jan 2014
Journal: Numerical Algorithms
Authors: , , ,
Keywords: homotopy method, optimal control, Chebyshev
Abstract:

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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