Behavioral Harmonization of a Cyclic Vehicular Platoon in a Closed Road Network

This paper presents a method to dynamically harmonize the behaviors of cyclic vehicular platoons in a closed road network. Different from the open-chain counterpart, a cyclic platoon formulates a traffic flow ring constrained by interconnection coupling feature and finite-length geometry, which brings challenges for platoon control design and analysis. First, by exploiting the circulant structure of homogeneous cyclic platoons, the closed-loop dynamics is decomposed into a set of decoupled systems with the same low dimension as a single vehicle. Based on this decomposition, an analytical necessary and sufficient stability condition is derived for the design of distributed feedback controllers. This necessary and sufficient condition is further relaxed into sufficient conditions to remove the dependence on the platoon size. Next, the string stability is proved with the sufficient conditions derived above based on frequency-domain analysis. Then, based on integral sliding mode control, we prove that heterogeneous vehicles can behave like homogeneous ones so that the results on homogeneous cyclic platoons can be extended to heterogeneous cyclic platoons. Finally, the equilibrium velocity and spacing errors are derived to explain the effect of geometry conditions on the steady-state behavior. Numerical simulations using both linear and nonlinear vehicle models are conducted to validate our findings.