Traffic-responsive control approaches, including model-predictive control (MPC), are efficient methods for making the best use of the available network capacity. Moreover, gradient-based approaches, which can be applied to smooth optimization problems, have proven their efficiency, both computationally and performance-wise, in finding optima of optimization problems. In this paper, we propose an MPC system for an urban traffic network that applies a gradient-based optimization approach to solve the control optimization problem. The controller uses a new smooth integrated flow-emission model to find a balanced tradeoff between reduction of the congestion and of the total emissions. We also introduce efficient smoothening methods for nonsmooth mathematical models of physical systems. The effectiveness of the proposed approach is demonstrated via a case study.@en

Nowadays, congestion caused by traffic in urban areas is considered as a major problem. In order to make the best use of the existing road capacity traffic-responsive control systems, including model-predictive controllers, are excellent choices. A mo del-predictive controller can minimize a cost function along a given time horizon. We propose a model-predictive control system that aims to reduce the congestion, and uses an internal flow model, which is our proposed modified version of the S-model. In the formulation of the objective function for the controller, we take into account the effect of those vehicles that remain in the network at the end of the prediction horizon until the network is completely evacuated. We formulate this effect as endpoint penalties for the MPC optimization problem. Finally, we will apply the designed controller to an urban traffic network and compare two scenarios, i.e., the fixed-time control case and the model-predictive control approach with the endpoint penalties proposed in this paper. The results prove the excellent performance of the model-predictive controller compared with the fixed-time controller.@en

To deal with the traffic congestion and emissions, traffic-responsive control approaches can be used. The main aim of the control is then to use the existing capacity of the network efficiently, and to reduce the harmful economical and environmental effects of heavy traffic. In this paper, we design a highly efficient model-predictive control system that uses a gradient-based approach to solve the optimization problem, which has been reformulated as a two-point boundary value problem. A gradient-based approach computes the derivatives to find the optimal value. Therefore, the optimization problem should involve only smooth functions. Hence, for nonsmooth functions that may appear in the internal model of the MPC controller, we propose smoothening approaches. The controller then uses an integrated smooth flow and emission model, where the control objective is to reduce a weighted combination of the total time spent and total emissions of the vehicles. We perform simulations to compare the efficiency and the CPU time of the smooth and nonsmooth optimization approaches. The simulation results show that the smooth approach significantly outperforms the nonsmooth one both in the CPU time and in the optimal objective value.

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