A contraction-constrained distributed MPC for heterogeneous vehicle platoons with explicit string stability

Heterogeneous vehicle platoons with nonlinear dynamics make it difficult to translate frequency-domain string-stability metrics into constraints that can be enforced online. To address this issue, this paper proposes a contraction-constrained distributed model predictive control strategy for heterogeneous platoons. In each local optimization problem, a time-domain contraction inequality is introduced to bound the finite-horizon mismatch between the predicted and assumed spacing-error trajectories. Together with the established closed-loop conditions, the resulting contraction mechanism provides an explicit, solver-embeddable route to predecessor-wise peak-error non-amplification. A terminal constraint set is further incorporated to guarantee asymptotic consensus, and sufficient conditions for recursive feasibility and string stability are established via Lyapunov analysis. Comparative simulations against a baseline that removes the contraction constraint demonstrate that the proposed strategy effectively suppresses spacing-error amplification under acceleration, deceleration, and multi-stage speed-change scenarios, while maintaining stable performance under platoon-size scaling.