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Abstract-In this paper, an advanced control strategy, i.e. Model Predictive Control (MPC), is applied to control and coordinate urban traffic networks. However, due to the nonlinearity of the prediction model, the optimization of MPC is a nonlinear non-convex optimization problem. In this case, the online computational complexity becomes a big challenge for the MPC controller, if it is implemented in real-life traffic network. To overcome this problem, the on-line optimization problem is reformulated into a Mixed-Integer Linear Programming (MILP) optimization problem, so as to increase the real-time feasibility of the MPC control strategy. The new optimization problem can be solved very efficiently by existing MILP solvers, and the global optimum of the problem is guaranteed. Moreover, we propose an approach to reduce the complexity of the MILP optimization problem even further. The simulation results show that the MILPbased MPC controllers can reach the same performance, but the time taken to solve the optimization becomes only a few seconds, which is a significant reduction compared with the time required by the original MPC controller.Index Terms-Urban traffic network control, Model predictive control, Urban traffic modeling.

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For the constrained uncertain systems with polytopic description, a new design method of robust feedback model predictive control is proposed. By using a sequence of feedback control laws and designing the parameterdependent Lyapunov function for each model, the design method provides more degrees of freedom and then can improve the control performance and enlarge the feasible region. Based on the characteristic property of the design method, an offline design algorithm is developed to reduce the MPC controller's online computation burden. The numerical examples verify the effectiveness of the results presented in this article.

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Network-wide control of large-scale urban traffic networks using a hierarchical framework can be more efficient and flexible than centralized strategies for reducing the traffic congestion in big cities, because it can adequately address some problems that occur in controlling such large systems, e.g., computational complexity, multiple control objectives, weak robustness to uncertainties, and so on. In this paper, we propose a two-level hierarchical control framework for large-scale urban traffic networks. At the upper level, based on decomposing a heterogeneous traffic network into several homogeneous subnetworks, a higher level optimization problem using the concept of macroscopic fundamental diagram is formulated to deal with the traffic demand-balance problem. At the lower level, the controller with a more detailed traffic flow model for each subnetwork determines the optimal signal timing within the given region under the guidance of the upper-level controller through communication. For the application of this architecture in real time, the model-based predictive control approach is utilized so as to obtain the best solutions for both levels. Moreover, in order to decrease the computational complexity, a distributed control scheme within each subnetwork is developed at the lower level. The proposed approach is evaluated by simulation under different scenarios on a hypothetical urban traffic network, and the performance is compared with that of other control strategies. Index Terms-Hierarchical control, large-scale urban traffic networks, macroscopic fundamental diagram (MFD), model predictive control (MPC). His current research interests include the multilevel control for large-scale urban traffic networks, and distributed optimization. Bart De Schutter (M'08-SM'10) received the M.Sc. degree in electrotechnical-mechanical engineering and the Ph.D. (summa cum laude) degree in applied sciences from the Katholieke Universiteit Leuven, Leuven, Belgium, in 1991 and 1996, respectively. He is currently a Full Professor with the Delft