Some numerical results using Kalaba´s new approach to optimal control and filtering

Numerical results are given comparing Kalaba´s new approach with a classical method for evaluating a simple optimal control problem. Kalaba´s new approach is to convert the optimal control problem directly into an initial-value problem without utilizing the Euler equations, Pontryagin´s maximum principle, or the principle of optimality. The classical method utilizes the calculus of variations to obtain the Euler equations with the two-point boundary conditions. The results show that five-digit accuracy or better is obtained using Kalaba´s approach, whereas the classical method gives large errors for large values of the terminal time.