Adaptive Backstepping Control for Nonlinear Vehicles With Guaranteed String Stability and Suppressed Cascade Fluctuations

Recent efforts have yielded substantial progress in backstepping platoon control for connected and automated vehicles (CAVs). While most existing studies focus on guaranteeing individual vehicle stability and string stability, their deployment in nonlinear vehicle platoons may face challenges from the so-called "butterfly effect." That is, even with guaranteed string stability, potential instantaneous spacing changes may imply unpredictable, uncomfortable fluctuations in vehicular velocity and acceleration. To address this issue, a parallel error-fluctuation suppression control framework is proposed in this work. Specifically, tunable triple-layered error boundaries (i.e., spacing, velocity, and acceleration) are constructed to reactively confine all propagated errors within predefined envelopes. By integrating a Barbalat-lemma-enhanced filtering-compensating mechanism and an adaptive approach based on the approximation capability of radial basis function neural networks (RBFNNs), asymptotic error tracking is realized to proactively suppress potential fluctuations. An adaptive backstepping control approach-integrating proactive and reactive suppression strategies-is then proposed to mitigate the unquantifiable "butterfly effect." Theoretical analysis and simulations demonstrate the validity and superiority of the proposed approach.