The Method of Deterministic Optimal Control with Box Constraints

A new method for deterministic optimal control problems with box constraints would be introduced. The new algorithm is based on the combination of Pontryagin Maximum principle and Projected Newton Method. The main idea of this method is introducing a minor control variable in order an open set instead of the original closed set. This new method has conquered the curse of dimensionality effectively. Moreover, this algorithm is almost super-linear convergent.