In this thesis, the primary powertrain components of a power split hybrid electric vehicle are modeled. In particular, the dynamic model of the energy storage element (i.e., traction battery) is exactly linearized through an input transformation method to take advantage of the proposed optimal control algorithm. A lipschitz continuous and nondecreasing cost function is formulated in order to minimize the net amount of consumed fuel. The globally optimal solution is obtained using a dynamic programming routine that produces the optimal input based on the current state of charge and the future power demand. It is shown that the global optimal control solution can be expressed in closed form for a time invariant and convex incremental cost function utilizing the interval back propagation approach. The global optimality of both time varying and invariant solutions are rigorously proved. The optimal closed form solution is further shown to be applicable to the time varying case provided that the time variations of the incremental cost function are sufficiently small. The real time implementation of this algorithm in Simulink is discussed and a 32.84 % improvement in fuel economy is observed compared to existing rule based methods.