  CAV platooning technology has received considerable attention in the past few
years, driven by the next generation smart transportation systems. Unlike most
of the existing platooning methods that focus on linear vehicle dynamics of
CAVs, this paper considers nonlinear vehicle dynamics and develops fully
distributed optimization based CAV platooning control schemes via the model
predictive control (MPC) approach for a possibly heterogeneous CAV platoon. The
nonlinear vehicle dynamics leads to several major difficulties in distributed
algorithm development and control analysis and design. Specifically, the
underlying MPC optimization problem is nonconvex and densely coupled. Further,
the closed loop dynamics becomes a time-varying nonlinear system subject to
external perturbations, making closed loop stability analysis rather
complicated. To overcome these difficulties, we formulate the underlying MPC
optimization problem as a locally coupled, albeit nonconvex, optimization
problem and develop a sequential convex programming based fully distributed
scheme for a general MPC horizon. Such a scheme can be effectively implemented
for real-time computing using operator splitting methods. To analyze the closed
loop stability, we apply various tools from global implicit function theorems,
stability of linear time-varying systems, and Lyapunov theory for
input-to-state stability to show that the closed loop system is locally
input-to-state stable uniformly in all small coefficients pertaining to the
nonlinear dynamics. Numerical tests on homogeneous and heterogeneous CAV
platoons demonstrate the effectiveness of the proposed fully distributed
schemes and CAV platooning control.
