Control of Freeway Traffic Flow in Unstable Phase by $H_{\infty }$ Theory

This paper devises a freeway controller that is capable of stabilizing traffic flow when the traffic system is in the unstable (congested) phase, in which a shock wave is likely to occur in the presence of any inhomogeneity and where the system is on the verge of a jam condition. Two types of traffic controllers are developed through the use of either a speed command approach that can be implemented in an intelligent transportation system (ITS) or ramp metering that is a typical way of preventing a freeway from overloading. By means of the feedback linearization technique, the discretized macroscopic traffic flow model is reformulated, in which the desired change of volume in each section is treated as a virtual input. By exploring the casual relations among density, speed, and flow change, the corresponding speed commands can be determined. The traffic flow control problem is formulated as an H_infin control design problem so that uncertainties that are associated with the macroscopic model can be taken into account. Simulations show that the devised controller can effectively stabilize the traffic flow in the unstable phase. Design flexibilities associated with the method are also discussed.