Hybrid electric vehicles provide promising alternatives to conventional engine-powered vehicles, offering improvements in fuel economy and emissions. Realization of these benefits depends, in part, upon proper control of the vehicle. This paper examines a variable structure control which switches between two operating points. The resulting sliding optimal control provides a better energy management strategy than that obtained conventionally from Pontryagin’s minimum principle. One of the operating points is zero engine power, thus the sliding optimal control is referred to as engine start-stop. Contrary to the general impression that the engine should stop at low speeds or during decelerations, new studies show that engine start-stop also improves fuel economy during highway cruising. The main contribution of this paper is to show that this “duty-cycle” operation mode is indeed optimal. The main tool used in the proof is Pontryagin’s minimum principle.

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