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.
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