Numerical solution of time-delayed optimal control problems by iterative dynamic programming

This work presents a numerical method to solve the optimal control problem with time-delayed arguments and a fixed terminal time. A series of auxiliary states obtained from the linearly truncated Taylor series expansion are used to represent the status of a time-delayed state at different time intervals. The backward iterative dynamic programming (IDP) technique can thus be directly employed to solve the delay-free optimal control problem with augmented states. Five numerical examples are provided, demonstrating the proposed method's effectiveness in solving the time-delayed optimal control problems.