An efficient discretization scheme for solving nonlinear optimal control problems with multiple time delays. (14th July 2015)

• Record Type: Journal Article
• Authors: Marzban, H. R.; Hoseini, S. M.
• Is Part Of: Optimal control applications and methods. Volume 37:Number 4(2016:Jul./Aug.)
• Page Start: 682
• Page End: 707
• Publication Date: 2015-07-14
• Subjects: nonlinear multi‐delay -- optimal control -- composite Chebyshev finite difference -- hybrid functions -- Chebyshev Gauss–Lobatto points; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2187
• Languages: English
• ISSNs: 0143-2087

Abstract

Summary: This paper presents a composite Chebyshev finite difference method to numerically solve nonlinear optimal control problems with multiple time delays. The proposed discretization scheme is based on a hybrid of block‐pulse functions and Chebyshev polynomials using the well‐known Chebyshev Gauss–Lobatto points. Our approach is an extension and also a modification of the Chebyshev finite difference scheme. A direct approach is used to transform the delayed optimal control problem into a nonlinear programming problem whose solution is much more easier than the original one. Some useful error bounds are established. In addition, the convergence of the method is discussed. A wide variety of numerical experiments are investigated to show the usefulness and effectiveness of the proposed discretization procedure. The method has a simple structure and can be implemented without too much effort. Copyright © 2015 John Wiley & Sons, Ltd.