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.