Stability Analysis of Vehicle Platooning With Limited Communication Range and Random Packet Losses

Abstract

Control performance of vehicle platooning relies on the information flow topology and quality of wireless communications. In this article, we investigate the constant-time-headway-spacing-policy-based vehicle platooning problem, where multiple predecessors' information is used by the following vehicles and communication impairments, i.e., limited communication range and random packet losses, are considered. In this article, first, when the leading vehicle moves at a constant speed, we obtain the sufficient and necessary conditions on sampling time, control gains, and internal lag, to ensure the stability of the vehicle platoon based on matrix polynomials' stability for ideal communications. Second, for time-independent homogeneous random packet losses, we provide the upper bound for the loss rate to maintain convergence in expectation by matrix eigenvalue perturbation theory when no input is set for lossy information. We also provide sufficient conditions to guarantee mean-square convergence for heterogeneous time-independent random packet losses and show the convergence time for any given accuracy and probability. Third, when historically latest information is used for input, the sufficient and necessary conditions are provided to ensure the internal stability and string stability by Markov jump linear system theory. Furthermore, we discuss the controller design when no feasible solution exists to guarantee the string stability. Extensive numerical results validate our analysis.