DistributedH∞ Controller Design and Robustness Analysis for Vehicle Platooning Under Random Packet Drop

Abstract

This paper presents the design of a robust distributed state-feedback controller in the discrete-time domain for homogeneous vehicle platoons with undirected topologies, whose dynamics are subjected to external disturbances and under random single packet drop scenario. A linear matrix inequality (LMI) approach is used for devising the control gains such that a bounded <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> norm is guaranteed. Furthermore, a lower bound of the robustness measure, denoted as <inline-formula> <tex-math notation="LaTeX">$\gamma $ </tex-math></inline-formula> gain, is derived analytically for two platoon communication topologies, i.e., the bidirectional predecessor following (BPF) and the bidirectional predecessor leader following (BPLF). It is shown that the <inline-formula> <tex-math notation="LaTeX">$\gamma $ </tex-math></inline-formula> gain is highly affected by the communication topology and drastically reduces when the information of the leader is sent to all followers. Finally, numerical results demonstrate the ability of the proposed methodology to impose the platoon control objective for the BPF and BPLF topology under random single packet drop.