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Connected and automated vehicles (CAVs) have a great potential to improvetraffic efficiency in mixed traffic systems, which has been demonstrated bymultiple numerical simulations and field experiments. However, some fundamentalproperties of mixed traffic flow, including controllability andstabilizability, have not been well understood. This paper analyzes thecontrollability of mixed traffic systems and designs a system-level optimalcontrol strategy. Using the Popov-Belevitch-Hautus (PBH) criterion, we provefor the first time that a ring-road mixed traffic system with one CAV andmultiple heterogeneous human-driven vehicles is not completely controllable,but is stabilizable under a very mild condition. Then, we formulate the designof a system-level control strategy for the CAV as a structured optimal controlproblem, where the CAV's communication ability is explicitly considered.Finally, we derive an upper bound for reachable traffic velocity viacontrolling the CAV. Extensive numerical experiments verify the effectivenessof our analytical results and the proposed control strategy. Our resultsvalidate the possibility of utilizing CAVs as mobile actuators to smoothtraffic flow actively.

Controllability Analysis and Optimal Control of Mixed Traffic Flow with Human-driven and Autonomous Vehicles