Leader and Predecessor Following Robust Controller Synthesis for String Stable Heterogeneous Vehicle Platoons

Abstract

Conditions of string (in)stability for look-ahead interconnected vehicle systems are presented based on a compact characterization of the interconnected system. Continuous-time local models describe the temporal evolution of the state-variables of one vehicle. Discrete spatially varying systems describe the spatial evolution of local systems. The problem of string stability analysis of large scale interconnected systems is reduced to the stability analysis of two simple dynamic systems. The evaluation of worst-case spacing errors, as responses to bounded L 2 leader acceleration, can be upper-bounded by computing the step-response to a simple discrete linear system. Based on the compact characterization, it is also shown that the string stability requirement can be directly converted to a standard H ∞ control problem. The efficiency of the synthesis method is demonstrated on a numerical example.

An Adaptive Spacing Policy Guaranteeing String Stability in Multi-Brand <italic>Ad Hoc</italic> Platoons

“…This implies that string stability of the platoon is related to the stability of discrete (in the spatial index i) linear systems where the variation of the coefficients is due to the heterogeneity of the platoon. The following theorem is a straightforward adaptation of [28,Theorem 1].…”

“…Uniform boundedness of a i in the L 2 norm is equivalent to the uniform boundedness of transfer functions G i in the H ∞ norm. Technical details can be found in [28]. The proof is based on the fact that for every ω the solution of the one-dimensional linear system with bounded spatiallyvarying uncertainty and bounded input is bounded if and only if the system is robustly stable with respect to the spatial variations.…”