Neural approximations for feedback optimal control of freeway systems

The problem of clearing congestion situations in freeway traffic is addressed for both an N-stage and an infinite-stage control horizon (in the latter case, a receding-horizon control mechanism is used). Traffic is controlled by regulating the vehicle access to the freeway and by limiting the vehicle speed by means of variable message signs. To describe the traffic behavior, a “classical” macroscopic model, first proposed by Payne (1971), is adapted. Even though the problem is stated within a deterministic context, an optimal control law in feedback form is sought to react to unpredictable events. The resulting functional optimization problem is reduced to a nonlinear programming problem by constraining the control law to take on a fixed structure in which free parameters have to be optimized. For such a structure, a multilayer feedforward neural mapping is chosen. Simulation results show the effectiveness of the proposed method in two different case studies. For the simulation of the second case study, real traffic data are used, which allows one to very well represent critical traffic conditions on freeways