Single-Region Robust Perimeter Traffic Flow Control

In this paper, we propose a two-stage robust perimeter flow control policy to prevent congestion in single-region transport networks. We describe the single-region traffic dynamics by utilising the so-called Macroscopic or Network Fundamental Diagram (MFD or NFD), a nonlinear relation between network-wide mean flow and accumulation of vehicles. By using MFD relaxation conditions and structuring uncertainties, we reformulate the nonlinear flow dynamics to set of uncertain Linear Parametrically Varying (LPV) ones. In controller design stage one, we apply the concept of a two degree of freedom, induced L-2 norm minimising LPV controller. Within the generalised performance output, we include tracking performance to follow a pre-defined critical accumulation in uncertain model environment. Output feedback LPV controller ensures generalised disturbance attenuation conditions with appropriate gated input flow at the perimeter. Second, an optimal quadratic control allocation algorithm is employed to distribute the ordered flow to entrance link green stages (flow equivalent green time) in a number of candidate junctions at the perimeter of the network. The constrained allocation techniques complement the robust controller enabling real-time applicability of the proposed methodology. Finally, the proposed robust control scheme is tested and compared with a reference tracking bang-bang controller in macroscopic simulation. Results indicate the viability of the proposed LPV controller and its rapid and accurate tracking behaviour under highly uncertain parameters of the MFD.