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

2013 ◽  
Vol 65 (1) ◽  
pp. 171-194 ◽  
Author(s):  
H. Saberi Nik ◽  
S. Effati ◽  
S. S. Motsa ◽  
M. Shirazian
Keyword(s):  
Optimal Control ◽  
Homotopy Analysis Method ◽  
Optimal Control Problems ◽  
Nonlinear Optimal Control ◽  
Control Problems ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Spectral Homotopy Analysis Method

ANALYTIC-APPROXIMATE SOLUTION FOR A CLASS OF NONLINEAR OPTIMAL CONTROL PROBLEMS BY HOMOTOPY ANALYSIS METHOD

2013 ◽  
Vol 06 (02) ◽  
pp. 1350012 ◽  
Author(s):  
Sohrab Effati ◽  
Hassan Saberi Nik ◽  
Mohammad Shirazian
Keyword(s):  
Optimal Control ◽  
Homotopy Analysis Method ◽  
Optimal Control Problems ◽  
Measure Theory ◽  
Initial Boundary ◽  
Control Problems ◽  
Theory Method ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Quadratic Optimal Control

In this paper, we apply the homotopy analysis method (HAM) for nonlinear quadratic optimal control problems (OCP's). This method is employed to solve extreme conditions obtained from the Pontryagin's maximum principle (PMP). Applying the HAM, we in essence transfer a nonlinear two-point boundary value problem (TPBVP), into an infinite number of linear sub-problems, and then use the sum of the solutions of its first several sub-problems to approximate the exact solution. Note that such a kind of transformation does not need the existence of any small or large parameters in governing equation and initial/boundary conditions. The comparison of the HAM results with the Measure theory method, Modal series and collocation method solutions are made. Some illustrative examples are given to demonstrate the simplicity and efficiency of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document