  Traffic congestion has dire economic and social impacts in modern
metropolitan areas. To address this problem, in this paper we introduce a novel
type of model-free transactive controllers to manage vehicle traffic in highway
networks for which precise mathematical models are not available. Specifically,
we consider a highway system with managed lanes on which dynamic tolling
mechanisms can be implemented in real-time using measurements from the roads.
We present three incentive-seeking feedback controllers able to find in
real-time the optimal economic incentives (e.g., tolls) that persuade highway
users to follow a suitable driving behavior that minimizes a predefined
performance index. The controllers are agnostic with respect to the exact model
of the highway, and they are also able to guarantee fast convergence to the
optimal tolls by leveraging non-smooth and hybrid dynamic mechanisms that
combine continuous-time dynamics and discrete-time dynamics. We provide
numerical examples to illustrate the advantages of the different presented
techniques.
