  The emergence of Connected and Automated Vehicles (CAVs) promises better
traffic mobility for future transportation systems. Existing research mostly
focused on fully-autonomous scenarios, while the potential of CAV control at a
mixed traffic intersection where human-driven vehicles (HDVs) also exist has
been less explored. This paper proposes a notion of "1+n" mixed platoon,
consisting of one leading CAV and n following HDVs, and formulates a
platoon-based optimal control framework for CAV control at a signalized
intersection. Based on the linearized dynamics model of the "1+n" mixed
platoon, fundamental properties including stability and controllability are
under rigorous theoretical analysis. Then, a constrained optimal control
framework is established, aiming at improving the global traffic efficiency and
fuel consumption at the intersection via direct control of the CAV. A
hierarchical event-triggered algorithm is also designed for practical
implementation of the optimal control method between adjacent mixed platoons
when approaching the intersection. Extensive numerical simulations at multiple
traffic volumes and market penetration rates validate the greater benefits of
the mixed platoon based method, compared with traditional trajectory
optimization methods for one single CAV.
