In this thesis:
• A power split hybrid electric vehicle is modeled as a linear system with respect to the state of charge through an input transformation method.
• A new dynamic programming approach called interval back propagation is introduced. This involves grouping discrete states into a set of specified intervals.
• A closed form globally optimal solution is obtained for the optimal input.
• The procedure used for real time implementation of the algorithm is elucidated
• The fuel economy results are compared with those from standard rule based techniques to confirm improvement.
A Lipschitz continuous cost function is modified so as to minimize the total amount of fuel consumed. An inductive proof then elucidates that the existence of a globally optimal solution using a dynamic programming routine is dependent on the nondecreasing, Lipschitz continuity, and convexity properties of f(ξ), which corresponds to convexity of the cost function. The proofs showing that f(ξ) indeed satisfies these properties are presented in sufficient detail to aid understanding. The interval back propagation algorithm is explained considering a time invariant cost, and proof of optimality has been derived. These conclusions are further extended to the time varying case by proving that variations from the optimum are sufficiently small. The real time implementation of this algorithm in Simulink is discussed, and fuel economy results obtained are validated. Under flat road conditions, a 52.7% improvement is seen in fuel economy across a variety of drive cycles.