Synthesis of intelligent control of traffic flows in urban roads based on the logical network operator method

A problem of optimal control of traffic flows in the urban network is considered. A derivation of the mathematical model of control by the traffic lights at intersections is given. The mathematical model of control object is obtained using the controlled networks theory. This model is a system of nonlinear finite-difference equations. To present a large scale road networks the model contains the connection matrices. The connection matrices describe connections between input and output roads in subnetworks. These matrices allow considering the influence of traffic flows in one subnetwork the ones in other subnetwork. The traffic flow control is done by the coordination of active phases of traffic lights. The optimal control problem is to minimize the difference between the total input flow and total output flow for all subnetworks. To solve the optimal control synthesis problem we use a logical network operator method. An example of model for the network of three subnetworks is given.