Abstract-Since centralized control of urban networks with detailed modeling approaches is computationally complex, developing efficient hierarchical control strategies based on aggregate modeling is of great importance. The dynamics of a heterogeneous large-scale urban network is modeled as R homogeneous regions with the macroscopic fundamental diagrams (MFDs) representation. The MFD provides for homogeneous network regions a unimodal, low-scatter relationship between network vehicle density and network space-mean flow. In this paper, the optimal hybrid control problem for an R-region MFD network is formulated as a mixed-integer nonlinear optimization problem, where two types of controllers are introduced: 1) perimeter controllers and 2) switching signal timing plans controllers. The perimeter controllers are located on the border between the regions, as they manipulate the transfer flows between them, while the switching controllers influence the dynamics of the urban regions, as they define the shape of the MFDs and as a result affect the internal flows within each region. Moreover, to decrease the computational complexity due to the nonlinear and nonconvex nature of the optimization problem, we reformulate the problem as a mixed-integer linear programming (MILP) problem utilizing piecewise affine approximation techniques. Two different approaches for transformation of the original model and building up MILP problems are presented, and the performances of the approximated methods along with the original problem formulation are evaluated and compared for different traffic scenarios of a two-region urban case study.Index Terms-Hybrid systems, macroscopic fundamental diagram (MFD), model predictive control (MPC), perimeter control, switching timing plans, urban traffic control.

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SUMMARYThis paper presents robust switching control strategies for switched nonlinear systems with constraints on the control inputs. A quantization technique is used to relax the constraint on continuous control inputs and the L 2 -gain analysis and H 1 control design problem for switched nonlinear systems are presented. Next, as an alternative method, the switched nonlinear system is approximated by a switched affine system that has autonomous and controlled switching behavior. A robust switching control law is proposed to stabilize the switched affine system. The design procedure involves solving an optimization problem that is nonconvex in a single scalar variable only. Furthermore, we provide the sufficient conditions under which the proposed switching law is able to stabilize the original switched nonlinear system. Finally, the proposed methods are utilized for control of urban traffic networks modeled on a high level. The traffic control objective is translated into a stability and disturbance attenuation problem for the urban network represented by a switched nonlinear system. The switching control approaches are able to reduce congestion in the network and to attenuate the effects of uncertain trip demands. Because the design of the switching laws is performed offline, real-time traffic control is possible with the proposed methods.

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