An optimal control problem in determining the optimal reinforcement schedules for the Lanchester equations

An optimal control problem for the Lanchester equations by utilizing the iterative regularization method, i.e. a nonparametric conjugate gradient method (NP-CGM), with adjoint equations is illustrated to determine the optimal reinforcement schedules based on the desired (or required) force strengths at some specified time. The numerical simulations are performed to test the validity of the present algorithm by using three different types of force strength requirements. Results show that the method is powerful enough to yield desired strengths at all points during the battle. Moreover, the advantages of applying the NP-CGM in the optimal control calculations lie in that (i) the initial guesses of the reinforcement schedules can be chosen arbitrarily and (ii) the optimal time-dependent reinforcement schedules can be determined within a very short computer time.