Numerical method based on extended one-step schemes for optimal control problem with time-lags

In this paper, we develop extended one-step methods for solving optimal control problem for systems governed by delay differential equations(DDEs). The optimal control problem governed by ordinary differential equations have been considered in this paper as a case of the DDEs with the absence of delays. The proposed problem is reduced to either a constrained or unconstrained minimization problem according to the nature of the dynamic system and the given conditions. Pontryagin’s maximum (or minimum) principle is used to characterize the optimal controls. Numerical results with simulations compared with other methods are presented to show the efficiency of the methodology.