Robustness Analysis of Platoon Control for Mixed Types of Vehicles

Currently, with the development of driving technologies, driverless vehicles gradually are becoming more and more available. Therefore, there would be a long period of time during which self-driving vehicles and human-driven vehicles coexist. However, for a mixed platoon, it is hard to control the formation due to the existence of the manual vehicles resulting in weak robustness and slow consensus rate on this system of platoons because of uncertainties caused by human factors for manual vehicles. In order to solve this problem, we establish models of mixed platoons with mixed types of connected and automated vehicles (CAVs), human-driven vehicles (HDVs) and HDVs without the vehicle awareness device (HDVWs). We subsequently design <inline-formula> <tex-math notation="LaTeX">$\mathcal{H}_\infty$</tex-math> </inline-formula> controllers for the mixed platoons to realize the formation consensus. In addition, we use the <inline-formula> <tex-math notation="LaTeX">$\mathcal{H}_\infty$</tex-math> </inline-formula> norm of mixed platoons as the control objective investigating the robustness of the control algorithms in alleviating the platoon uncertainties. Furthermore, conditions are proved to maintain the stability of the mixed platoons, and the stability is analyzed based on the variation of the penetration rate of the manual vehicles. Finally, we formulate conditions for parameters according to the definition of string stability to avoid the collisions of vehicles. The results in this study are tested with simulations and suggest that the presented controllers can ensure the consensus of mixed platoons under uncertainties.