An approximate method for solving a class of nonlinear optimal control problems

• Published in: Optimal control applications & methods Vol. 35; no. 3; pp. 324 - 339
• Main Authors: Saberi Nik, H., Effati, S.
• Format: Journal Article
• Language: English
• Published: Glasgow Blackwell Publishing Ltd 01.05.2014; Wiley Subscription Services, Inc
• Subjects: Computation; differential transform method; DT's polynomials; Mathematical analysis; Mathematical models; Matlab; nonlinear optimal control problems; Nonlinearity; Optimal control; Polynomials; Pontryagin's maximum principle; Transforms
• ISSN: 0143-2087; 1099-1514
• DOI: 10.1002/oca.2070

SUMMARYThis 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.