An efficient discretization scheme for solving nonlinear optimal control problems with multiple time delays

作者：Marzban H R^*; Hoseini S M

来源：Optimal Control Applications and Methods, 2016, 37(4): 682-707.

DOI：10.1002/oca.2187

• nonlinear multi-delay
• optimal control
• composite Chebyshev finite difference
• hybrid functions
• Chebyshev Gauss-Lobatto points

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.

• 出版日期2016-8