Distributionally Robust Optimization Based Model Predictive Control for Stochastic Mixed Traffic Flow

In this paper, we investigate a mixed-traffic control problem considering uncertainties of HDVs flow. The challenges mainly lie in modeling the stochastic characteristics of mixed-traffic flow and developing less-conservative algorithm to deal with the uncertainties. To tackle the problem, we propose a stochastic model predictive control (MPC) strategy based on data-driven distributionally robust optimization (DRO). First, a stochastic mixed-traffic model, extended from cell transmission model, is proposed to describe the traffic dynamics. Then, utilizing historical traffic data, an incremental principal component analysis (IPCA) based method is given to construct ambiguity set and incorporate generalized moment information of uncertainties. Based on the above predictive model and ambiguity set, a DRO-based MPC problem is formulated and further converted into an equivalent dual form for efficient solutions, i.e., ramp metering and variable speed limit control. Finally, simulation results based on real data collected in Shanghai, China, demonstrate that our proposed strategy can significantly reduce traffic congestion, achieving 5.74 \% total travel time reduction compared to robust MPC.