Nash Game-Based Distributed Control Design for Balancing Traffic Density Over Freeway Networks

In this paper, we study the problem of optimal balancing of vehicle density in freeway traffic. The optimization is performed in a distributed manner by utilizing the controllability properties of the freeway network represented by the Cell Transmission Model. By using these properties, we identify the subsystems to be controlled by local ramp meters. The optimization problem is then formulated as a noncooperative Nash game that is solved by decomposing it into a set of two-players hierarchical and competitive games. The process of optimization employs the communication channels matching the switching structure of system interconnectivity. By defining the internal model for the boundary flows, local optimal control problems are efficiently solved by utilizing the method of linear quadratic regulator. The developed control strategy is tested via numerical simulations in two scenarios for uniformly congested and transient traffic.