Optimal Control Methodologies for Urban Eco-Driving of Electric Vehicles With Regenerative Braking

As a part of the global plan to achieve environmental sustainability, eco-driving defines a set of driving behaviors that benefit both the drivers, by reducing fuel or energy consumption, and the environment, by mitigating emissions. This paper refers to urban eco-driving concepts for electric vehicles with regenerative braking, aiming to mitigate energy consumption on trajectories from their current state to a fixed final state. Such trajectories are determined as solutions of an optimal control problem having the acceleration of the electric vehicle as control input, and the position and speed as state variables. A power-based energy model is used to calculate the energy consumption and the energy regeneration while braking, resulting in a non-smooth model with some discontinuities. In order to solve the problem, different approaches are considered, based on different approximations of the power-based model. Such approaches are then extended to address the stop point problem, considering a traffic signal placed on the way of the vehicle. A comparative analysis is reported and discussed in the paper for different initial state and signal timing scenarios. In particular, it is shown that the analytical solutions obtained using a quadratic approximation of the energy model are very similar to the numerical solutions but they can be obtained with less computational effort, making them applicable in real-world applications.