Mean-Field of Optimal Control Problems for Hybrid Model of Multilane Traffic

Multilane traffic is hard to model because of its hybrid nature: continuous dynamics on each lane and discrete event for lane-change. We design a hybrid system, where the lane-changing mechanism has three components: safety, incentive and cool-down time. We model traffic flow using two populations: human-driven vehicles and autonomous vehicles. Recently, a lot of attention was given to control of traffic with autonomous vehicles. We consider the mean-field as one population (human-driven) pass to the limit. Gamma-convergence is proven for optimal control problems at the microscopic scale to the mean-field ones, consisting of coupled controlled hybrid ODEs and Vlasov-type PDE with source terms representing lane-change.