Controllability Analysis and Optimal Control of Mixed Traffic Flow With Human-Driven and Autonomous Vehicles

Abstract

This paper analyzes the controllability of mixed traffic systems and designs a system-level optimal control strategy. Using the Popov-Belevitch-Hautus (PBH) criterion, we prove for the first time that a ring-road mixed traffic system with one CAV and multiple heterogeneous human-driven vehicles is not completely controllable, but is stabilizable under a very mild condition. Then, we formulate the design of a system-level control strategy for the CAV as a structured optimal control problem, where the CAV’s communication ability is explicitly considered. Finally, we derive an upper bound for reachable traffic velocity via controlling the CAV. Extensive numerical experiments verify the effectiveness of our analytical results and the proposed control strategy. Our results validate the possibility of utilizing CAVs as mobile actuators to smooth traffic flow actively.