In predictive adaptive cruise control systems, a major challenge is estimating the future driving pattern of the lead car. This paper proposes an adaptive cruise control system that acts more smoothly and fuel efficiently by utilizing probabilistic information of velocity transition of the front car. The car following problem is formulated in a chance constrained model predictive control framework in which the inter-vehicle gap constraints are enforced probabilistically. The probability distribution of the position of the front car is estimated through a Markov Chain Monte Carlo (MCMC) simulation. The position probability distribution is then utilized to convert the chance constrained MPC problem to a deterministic linear MPC problem. Two case studies with two real driving cycle profiles are presented to show the potential improvement in fuel economy.

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