A PDE-based approach to formation control design for a large vehicular platoon

This paper considers the problem of formation control design for a large platoon of identical vehicles, where the dynamics of each vehicle is described by a fully actuated double integrator. The main objective of this paper is to design a formation controller for the vehicular platoon under a nearest-neighboring communication topology maintaining a desired formation. Partial differential equations (PDEs) of the second-order time derivative are employed to approximately describe the closed-loop collective dynamics of the platoon. In the light of mathematical tools for analyzing PDE, a simple but effective design method has been developed based on the obtained PDE model, and presented in term of spatial algebraic linear matrix inequalities (SALMIs) and LMIs. Finally, some simulation results are given to verify the effectiveness of the suggested formation control design methods.