2020/06/16 by Uroš Kalabić, Kalabić, Uroš, Piyush Grover +3
Engineering · Social Sciences · #FOS: Mathematics #Optimization and Control (math.OC) #Traffic control and management #Transportation Planning and Optimization
paper · pdf · doi:10.48550/arxiv.2006.09622
openalex publication_date 2020/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of incentivization and optimal control of autonomous\nvehicles for improving traffic congestion. In our scenario, autonomous vehicles\nmust be incentivized in order to participate in traffic improvement. Using the\ntheory and methods of optimal transport, we propose a constrained optimization\nframework over dynamics governed by partial differential equations, so that we\ncan optimally select a portion of vehicles to be incentivized and controlled.\n The goal of the optimization is to obtain a uniform distribution of vehicles\nover the spatial domain. To achieve this, we consider two types of penalties on\nvehicle density, one is the L2 cost and the other is a multiscale-norm cost,\ncommonly used in fluid-mixing problems. To solve this non-convex optimization\nproblem, we introduce a novel algorithm, which iterates between solving a\nconvex optimization problem and propagating the flow of uncontrolled vehicles\naccording to the Lighthill-Whitham-Richards model. We perform numerical\nsimulations, which suggest that the optimization of the L2 cost is\nineffective while optimization of the multiscale norm is effective. The results\nalso suggest the use of a dedicated lane for this type of control in practice.\n