Article ID: | iaor2014222 |
Volume: | 65 |
Issue: | 1 |
Start Page Number: | 171 |
End Page Number: | 194 |
Publication Date: | Jan 2014 |
Journal: | Numerical Algorithms |
Authors: | Saberi Nik H, Effati S, Motsa S S, Shirazian M |
Keywords: | homotopy method, optimal control, Chebyshev |
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