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

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.