A hierarchical MPC and sliding mode based two-level control for freeway traffic systems with partial demand information

In this paper a hierarchical two-level control scheme is proposed in order to solve a ramp metering problem in freeway traffic systems. The proposal combines a Model Predictive Control (MPC) based supervisor with decentralized low-level Sliding Mode Controllers (SMCs). The considered freeway METANET model describes the traffic system, which is naturally affected by uncertainties since the mainstream inflow, the traffic demands on the on-ramps, and the flows exiting the off-ramps are not a priori known. In the proposed scheme, two control loops are present. A centralized MPC computes the optimal control inputs by minimizing the total time spent by the vehicles in the traffic system on the basis of a nominal model of the considered freeway stretch. The computed optimal inputs are used to generate the corresponding density references for the low-level on-ramp controllers, which rely on a saturated version of the Suboptimal Second-Order Sliding Mode (SSOSM) control algorithm. SSOSM controllers allow to regulate the density error to zero in a finite time, thus reducing the mismatch between the controlled traffic system dynamics and the model used by the MPC supervisor during the optimization. A simulation study encompassing several realistic scenarios is reported to assess the validity of the proposed approach also in comparison with other classical traffic control strategies. As confirmed by simulation, in spite of the uncertainties, the proposed control scheme produces satisfactory performance in terms of both total time spent minimization and capacity drop alleviation.