Smoothening for Efficient Solution of Model Predictive Control for Urban Traffic Networks Considering Endpoint Penalties

Traffic congestion together with emissions has become a big problem in urban areas. Traffic-responsive control systems aim to make the best use of the existing road capacity. Here, we propose a model-predictive controller for urban traffic networks, where the goal of the control is to find a balanced trade-off between reduction of congestion and emissions. The cost function is defined as a weighted combination of the total time spent, TTS, (as a criterion for evaluating the congestion level), the total emissions, TE, and the expected values of the TTS and TE caused by the vehicles that remain in the network at the end of the prediction horizon until they leave the network. We propose a method for estimation of the expected time spent and emissions by the remaining vehicles, where our method is based on a K Shortest path algorithm. For the prediction model of the MPC-based controller, we use a macroscopic integrated flow-emission model that includes the macroscopic flow S-model and the microscopic emission model, VT-micro. Since the S-model includes non-smooth functions, it does not allow us to benefit from efficient gradient-based methods to solve the optimization problem of the MPC-based controller. Therefore, in this paper we also propose smoothing methods for the S-model.