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As autonomous vehicles (AVs) become increasingly prevalent, their interactionwith human drivers presents a critical challenge. Current AVs lack socialawareness, causing behavior that is often awkward or unsafe. To combat this,social AVs, which are proactive rather than reactive in their behavior, havebeen explored in recent years. With knowledge of robot-human interactiondynamics, a social AV can influence a human driver to exhibit desired behaviorsby strategically altering its own behaviors. In this paper, we present a novelframework for achieving human influence. The foundation of our framework liesin an innovative use of control barrier functions to formulate the desiredobjectives of influence as constraints in an optimal control problem. Thecomputed controls gradually push the system state toward satisfaction of theobjectives, e.g. slowing the human down to some desired speed. We demonstratethe proposed framework's feasibility in a variety of scenarios related tocar-following and lane changes, including multi-robot and multi-humanconfigurations. In two case studies, we validate the framework's effectivenesswhen applied to the problems of traffic flow optimization and aggressivebehavior mitigation. Given these results, the main contribution of ourframework is its versatility in a wide spectrum of influence objectives andmixed-autonomy configurations.

An Optimal Control Framework for Influencing Human Driving Behavior in Mixed-Autonomy Traffic