Numerical solution of time-delayed functional differential equation control systems

We develop a pseudospectral approximation scheme for solving the class of time-delayed functional differential equation control systems. The problem is first formulated as a delay free optimal control problem governed by a system of partial differential equations with nonlocal boundary conditions. Next, a Chebyshev spectral method together with the cell-averaging Chebyshev integration technique are used to discretize the delay free optimal control problem. The optimal control problem is thereby transformed into a nonlinear programming problem which can be solved by well-developed nonlinear programming algorithms. Due to its dynamic nature, the proposed method avoids many of the numerical difficulties typically encountered in solving standard time-delayed optimal control problems. Moreover, a comparison is made with optimal solutions obtained by closed-form analysis and/or other numerical methods in the literature.