A new analytical method for solving a class of nonlinear optimal control problems

Abstract

SUMMARYIn this paper, we introduce a new analytic technique for a class of nonlinear optimal control problems and present a theorem of convergence of the method. In this scheme, first, the original optimal control problem is transformed into a nonlinear two‐point boundary value problem via the Pontryagin's maximum principle, and then, we apply a new method for solving two‐point boundary value problem. The proposed modification is made by introducing He's polynomials in the correction functional. The suggested algorithm is quite efficient and is practically well suited for using in these problems. The proposed iterative scheme finds the solution without any discretization, linearization, or restrictive assumptions. Copyright © 2013 John Wiley & Sons, Ltd.

On comparison between iterative methods for solving nonlinear optimal control problems

“…If we apply the ADM (Fakharian et al, 2010) or the HPM (Nik et al, 2012) to equation (35), we find same iterative formula that is given in Matinfar and Saeidy (2014) by using the VHPM.…”

“…Now we briefly describe an alternative approach of the variational iteration method (VIM) which is called MVIM (Matinfar and Saeidy, 2014) or VHPM (Matinfar and Ghasemi, 2010;. This method is proposed as the coupling of the VIM and the HPM.…”

“…Consider the following type of nonlinear OCP (Fakharzadeh, 2012;Matinfar and Saeidy, 2014;Nik et al, 2012) min J ¼…”

“…It is known that a nonlinear optimal control problem (OCP) can be converted to a Hamilton-Jacobi-Bellman (HJB) partial differential equation or a nonlinear two-point boundary value problem (TPBVP). Many researchers have attempted to solve these two problems (see Diehl et al, 2005;Fakharian and Behshti, 2008;Fakharian et al, 2010;Fakharzadeh, 2012;Ha¨ma¨la¨inen and Halme, 1976;Jajarmi et al, 2011;Manseur et al, 2005;Matinfar and Saeidy, 2014;Nik et al, 2012, and the references therein).…”

Development of the method of quasi-optimal robust control for periodic operational processes

“…At the same time, the issues of optimal control processes formalization and automation are in the experimental developments stage [5,6].…”