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We consider the problem of incentivization and optimal control of autonomousvehicles for improving traffic congestion. In our scenario, autonomous vehiclesmust be incentivized in order to participate in traffic improvement. Using thetheory and methods of optimal transport, we propose a constrained optimizationframework over dynamics governed by partial differential equations, so that wecan optimally select a portion of vehicles to be incentivized and controlled.  The goal of the optimization is to obtain a uniform distribution of vehiclesover the spatial domain. To achieve this, we consider two types of penalties onvehicle density, one is the $L^2$ cost and the other is a multiscale-norm cost,commonly used in fluid-mixing problems. To solve this non-convex optimizationproblem, we introduce a novel algorithm, which iterates between solving aconvex optimization problem and propagating the flow of uncontrolled vehiclesaccording to the Lighthill-Whitham-Richards model. We perform numericalsimulations, which suggest that the optimization of the $L^2$ cost isineffective while optimization of the multiscale norm is effective. The resultsalso suggest the use of a dedicated lane for this type of control in practice.

Optimization-based incentivization and control scheme for autonomous traffic