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Eco-driving at signalized intersections has significant potential for energy saving. In this paper, we focus on eco-departure operations of connected vehicles equipped with an internal combustion engine and a step-gear automatic transmission. A Bolza-type optimal control problem (OCP) is formulated to minimize engine fuel consumption. Due to the discrete gear ratio, this OCP is a nonlinear mixed-integer problem, which is challenging to handle by most existing optimization methods. The Legendre pseudospectral method combining the knotting technique is employed to convert it into a multistage interconnected nonlinear programming problem, which then solves the optimal engine torque and transmission gear position. The fuel-saving benefit of the optimized eco-departing operation is validated by a passenger car with a five-speed transmission. For real-time implementation, a near-optimal departing strategy is proposed to quickly determine the behavior of the engine and transmission. When a string of vehicles are departing from an intersection, the acceleration of the leading vehicle(s) should be considered to control the following vehicles. This issue is also addressed in this paper.
Li et al. (Tue,) studied this question.