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An approximate method for solving a class of nonlinear optimal control problems
Author(s) -
Saberi Nik H.,
Effati S.
Publication year - 2013
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2070
Subject(s) - nonlinear system , matlab , optimal control , simple (philosophy) , convergence (economics) , class (philosophy) , shooting method , mathematics , quadratic equation , differential (mechanical device) , function (biology) , mathematical optimization , computer science , mathematical analysis , boundary value problem , geometry , artificial intelligence , philosophy , physics , epistemology , quantum mechanics , aerospace engineering , evolutionary biology , engineering , economics , biology , economic growth , operating system
SUMMARY This paper presents a novel computational approach to generate the suboptimal solutions for a class of nonlinear optimal control problems (OCP's) with a quadratic performance index. Our method is based on the one‐dimensional differential transform method (DTM) and new polynomials that are called DT's polynomials. This method simplifies the difficulties and massive computational work for calculating the differential transform of nonlinear function. The convergence of proposed method are discussed in detail. This method consists of a new modified version of the DTM together with a shooting method such as procedure, for solving the extreme conditions obtained from the Pontryagin's maximum principle. The results reveal that the proposed methods are very effective and simple. Comparisons are made between new DTM generated results, results from literature, and MATLAB bvp4c generated results, and good agreement is observed. Copyright © 2013 John Wiley & Sons, Ltd.