On Implementation of Dynamic Programming for Optimal Control Problems with Final State Constraints

In this paper we present issues related to the implementation of dynamic programming for optimal control of a one-dimensional dynamic model, such as the hybrid electric vehicle energy management problem. A study on the resolution of the discretized state space emphasizes the need for careful implementation. A new method is presented to treat numerical issues appropriately. In particular, the method deals with numerical problems that arise due to high gradients in the optimal cost-to-go function. These gradients mainly occur on the border of the feasible state region. The proposed method not only enhances the accuracy of the final global optimum but also allows for a reduction of the state-space resolution with maintained accuracy. The latter substantially reduces the computational effort to calculate the global optimum. This allows for further applications of dynamic programming for hybrid electric vehicles such as extensive parameter studies.