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We present a predictive cruise controller which iteratively improves the fuel economy of a vehicle traveling along the same route every day. Our approach uses historical data from previous trip iterations to improve vehicle performance while guaranteeing a desired arrival time. The proposed predictive cruise controller is based on the recently developed Learning Model Predictive Control (LMPC) framework, which is extended in this paper to include time constraints. Moreover, we reformulate the modified LMPC with time constraint into a computationally tractable form. Our method is presented in detail, applied to the predictive cruise control problem, and validated through simulations.

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